Find out what the emergency numbers are in both countries. Make sure he has a local cell phone that will work in both countries. Teach him how to say, "I need emergency services, do you speak English" in French and Italian. Make sure he was an emergency 20 euro bill stashed. He should always carry his own passport. And give him a card with emergency numbers for stateside contacts, including international dialing codes. Teach him what international dialing codes are and why he needs to dial a different way there.

Has he ever taken a first aid course?

He'll be fine.

He should have access to a cellphone with a SIM card that will work in Italy and France, and he should know how to make calls with it--calls back to the US and calls within Italy/France. He should have, in several different places, the telephone number of the US embassy consular affairs office in Rome anf Paris and of the US consulates in or near other cities he will be visiting.

He'll need access to money, so either an ATM card or a credit card or both.

He should know how to answer the "Does your dad have medical insurance?" question.

He should know that, during their working hours, there will always be someone who speaks English well at the tourist office in any major tourist city. If he has a problem, they will understand what he is saying and will be able to direct him to the right place for substantive help. That's where I went when my mother became ill in Greece and I needed to know where to find English-speaking medical help. The front desk staff of 3-star or higher hotels is also likely to be able to assist with problems expressed in English.

I was very recently comparing travel insurance policies (medical/evacuation) for an upcoming trip, I noticed that most of the evacuation coverage included the costs of transport of a minor (with chaperone) back home in case of a serious medical incident involving the guardian. In addition there is also coverage for the costs of a "bedside" visit that will probably cover the expense of you going to Europe to collect your son.
So, at a minimum you should both have copies of the the emergency contact numbers for the insurance company. It would also be smart to register the trip with State Department's Step program so the consulate can get involved should something bad happen:
https://step.state.gov/

Have the teen carry an index card or business card with the hotel name/address and phone # and some cash. If he gets lost, teach him to take a taxi back to the hotel. Also, teach him "safe" places to go for help like the police or a tourist info. station or even a pharmacy/medical center. He should carry his own passport and have a copy of his dad's passport as well. He should carry your home contact info. also. His first priority should be to identify and go to a "safe" place. Even a business like a grocery store. Get a neck wallet/pouch for him to wear containing the info. or a money belt. Whatever is more comfortable for him to wear.

turn the question on its head and ask what would dad do if anything happened to the boy?

same practicalities would apply, emergency contact numbers both locally and U.S,, and money

store numbers in a phone in international format so to call US it would be +1 212 123 4567

What would you have him carry if the driving trip were through Oregon and California ? ID, medical insurance cards, phone numbers for you and medical professionals. Hotel owners/managers are often good sources of information and help. (I got a medical referral from the owner when I had a sudden hearing loss in Berlin.)

Will he and Dad have a working phone for emergency use? Hotel can most likely provide connection over their lines if needed (expensive, but in an emergency, useful.)
Is there a special reason you are concerned about "if the worst happened"?

Besides the suggestions above, I have a simple addition (that would work for most adults).

Save on your smartphone a couple of translated phrases in the lines of "I have a medical emergency with someone else, please help" translated. This is the best way to quickly get any stranger, or almost any stranger, to help you out.

Emergency number: 112 (click for details)

This is the emergency telephone number (police+ambulance+fire) in all European countries. It works in additional to each countries "traditional" numbers, so travellers only have to remember one number.
This is a free number, on mobile phones it will work even if you have no credit, or even no SIM card in the phone, but obviously not if the battery is flat. It is a legal requirement that it does work.

Give him a photocopy of his passport (or scan it in and put it in his phone), probably better if his dad keeps his passport. And an address card from the hotel he is staying at, though I realise with a driving trip this will keep changing.

Finally, don't panic, is is as unlikely that anything will happen as it is when his dad drives him to the local shops. And he will have the time of his life.

This is when you call the Consulate or Embassy for help. They will oversee arrangements.

While I like Laura B's helicopter-piloting advice, I also thought the mention of travel insurance was helpful: The insurances I have used have a collect-USA phone number where they handle travel emergencies, theoretically doing everything. (I haven't ever made a claim ... ) You will have to make sure your son has some way to make the call.

But honestly, if dad collapses on the sidewalk, the locals are going to call the emergency number for him. He can let the hospital social worker or the police call the collect number for him.

Sorry, I can't resist giving my two cents worth. With all due respect, I think most of your worrying and many of the suggestions are overkill. The only two things he needs are a way to communicate with his dad if they get separated (phone or email capability), and the presence of mind to remain calm and ask for help. In Italy and France, a huge % of people will speak English and be glad to help him. Don't weigh your son down with two many details and worries (e.g. pre canned phrases / plans about a bunch of different unlikely events). Just provide him an easy way to communicate with dad if separated, and presence of mind to ask for help. Ok, like I said, my two cents worth.

Minor traveling with only one parent:
http://www.us-passport-service-guide.com/minor-travel-consent-form.html

An immigration officer, airline, or travel company may ask for a
letter of consent if the child is traveling internationally with only
one parent or with another adult, such as a relative, friend, teacher,
etc.

Some samples of minor travel consent forms also include language allowing the single parent to consent to medical treatment of the minor with language such as:

I ALSO AUTHORIZE THE TRAVELING ADULT TO OBTAIN ANY NECESSARY MEDICAL
TREATMENT BY A LICENSED PHYSICIAN/ HOSPITAL/PHARMACY/ RESCUE SQUAD/
AMBULANCE COMPANY / MEDICAL AIR EVACUATION COMPANY.

IN THE EVENT THE TRAVELING ADULT IS INCAPACITATED AND CANNOT GIVE
AUTHORIZATION FOR TREATMENT, I AUTHORIZE A LICENSED PHYSICIAN/
HOSPITAL/ PHARMACY/ RESCUE SQUAD, AMBULANCE COMPANY /MEDICAL AIR
EVACUATION COMPANY TO GIVE MY CHILD(REN) ANY NECESSARY MEDICAL
TREATMENT. I CAN BE REACHED AT
_________________________________________________________ (Telephone Number) HOWEVER, I DO WANT TREATMENT TO COMMENCE PRIOR TO MY BEING
CONTACTED IF MY CHILD(REN) IS IN PAIN OR THE CONDITION IS LIFE
THREATENING.
http://www.singleparenttravel.net/wp-content/uploads/2009/06/Minor-Consent-Letter.pdf

When my kids were that age, they'd go with their dad to a fly in fishing camp in northern Ontario. Dropped off by a float plane at a cabin with no communication, they'd get picked up a week later. The advice given by the organizers is that in case of an emergency, light a small island on fire and the fire watchers will send a plane. Your son should probably not do that.

You should have one or two matter of fact conversations with your son, giving him a basic run down of who to call, etc. Any more than that and you'll likely freak him out. In Europe, his dad should give him some leeway and independence. Send him alone for breakfast or let him wander around a bit. That will give him the confidence that he can handle himself, and will reduce panic in an emergency.

Valuable post by Edgar.
Even if your son's father is in good health, it couldn't hurt to have medical travel insurance.
In fact, I'd suggest it for both of them.
...and I'd increase the amount of money to 100 EU.

Thank you, everyone, for such helpful advice. I particularly appreciate the advice to calm down.

Because a few of you asked, my son's dad is a very spontaneous traveler and my son is a great traveling companion, but, in a crisis, they both tend to get panicky and scattered. They are perfect if you want to explore a new location but not who you want in the emergency exit row.

I've used your excellent advice to create a checklist and we'll have a family meeting to make a plan.

Thank you again! This is my first post and I'm bowled over by the kindness of this community.

Also, based on your advice, I checked and they are covered by Redpoint insurance.

I'm also trying to remember that I was a terrible map reader until I was lost in Paris as a teen.

If (like me) one wants to be prepared for emergencies, and then not have to worry until they actually happen, here are some numbers to have available.

US Consulate in Rome: +39 06 46741
US Embassy in Paris: +33 1 43 12 22 22

AT&T USA Direct is a program where you dial a number (free call from a landline), and are connected with an English-speaking operator. This operator can then make a collect call to the US.

Access number in Italy: 800 172 444
Access number in France: 0800 99 0011

Oh goodness I agree with bob , a lot of overkill here .

I took my 13 yr old son alone to Europe .
I have also taken my 11 yr old daughter alone with me to Europe . Both trips were over 3 weeks long and involved several countries .

Sorry , my kids did not carry their own passports , I did , in my money belt while in transit and I hotel safe when not .

Both carried only school ID , copy of passport and ATM cards .

Both always had 20 or so euros on them .

Both always had Hotel card on them , if seperated from me for a long period of time they were to get in taxi to hotel . When we entered a busy area the instructions of separated from me were NOT to move , I would return to area we were last together . At museums they were to go to museums main entry .

Worst case scenario they were get police , police would contact embassy for them . I have a lot of faith that authorities in Europe are competent .

If your son should get separated from his father on the Metro, which is easy to do, have him get off at the next stop and wait underneath the clock.
This also goes for his father...