Inexpensive phone with French number.

Any phone (or SIM card) you buy in France will automatically have a French phone number. There are plenty of places you can buy cheap "pay-as-you go" phones or SIM cards, including supermarkets. You will have to provide ID and address when you buy.
Cheap phones start at about €20, but that will just be a phone, with possibly a camera, no GPS, data, translations or Internet.

An off-topic subject, is it not cheaper just to use your own phone? Most places in France (or Europe in General) will not mind that you give them a foreign phone number.

I was not aware that people would not mind calling a USA number. I assumed the charges to call a foreign number would be high and that I would be more likely to get a response with a French number. In addition, I have read horror stories online of people returning from an international trip to exorbitant phone bills. I will check further on the cost of using my own phone.

Thanks you for your suggestion.

The cheapest way to go is to buy a pay as you go phone once you arrive. I'm glad my US phone doesn't work as a phone in Europe - no problem with getting confirmation calls for dentist appointments, middle of the night calls from people who don't know you are traveling, etc. I use my US phone for WiFi internet access and buy a local phone for calls.

Lucy,
This weekend I have been seeing a lot of adverts for a package by a local phone company here in Switzerland. 49 Franks per month for unlimited calls to any number in Switzerland, the EU and the USA, plus data and SMS. In Europe international calls do not cost significantly more than national calls.
However I suspect it is otherwise in the USA, judging from the number of posts I have seen saying they "do not have an international plan", "cannot call numbers in Europe from their home phone" or are simply trying to save money by buying a SIM card in Europe.

Lucy, you can buy a cheap ($20-30) unlocked phone from Amazon that will work just fine in Europe. Taking it with you will save you the hassle of wasting valuable vacation time shopping for a phone. Once you arrive in Paris, pop into the first tabac you come to and buy a Lebara SIM card for 5 euros plus a 10 euro top-up card. Most, but not all tabacs carry Lebara. Back at your apartment, follow the instructions to reach an English speaking tech who will activate your SIM for you. The entire process takes less than 5 minutes. Lebara has very reasonable rates for calling the US as well as local calls. I've used this system on my last two trips to Paris and it works just fine. Have a great trip.

I respectfully disagree with Carolyn about buying a phone here and taking it with you. You have no way to check before your trip to make sure the phone is truly unlocked, or that it even has the correct bands for use in Europe. Everyone says you can get an unlocked phone for "$20-30", but I have never found one that cheap. When I was in the UK last year, Vodaphone had a pay as you go phone for ten pounds, and it came with a SIM that had, I think 9 pounds credit on it. Stopping into a phone store takes no longer than stopping to buy a SIM, and they can get it set up and working for you in minutes.

lucy,

One of the cheapest phone options in France will probably be Lebara. My suggestion would be to check into your hotel and then ask the desk staff for recommendations and where the nearest mobile phone shop is. I'm sure there will be one nearby, so you should have a working phone very quickly.

Another option would be to buy an inexpensive phone from one of the travel phone firms such as Roam Simple, Cellular Abroad, Telestial, Mobal, OneSIM, Max Roam or others (they run about $40). These usually have a U.K. number but will work all over Europe. This would provide you with a working phone as soon as you step off the plane.

If you're planning to use your own cell phone for "GPS, data, translations, etc.", I assume you're signing up for data roaming with your home cell network? Cellular data roaming without some type of roaming plan can be VERY expensive!

We bought a cheap cell for about 20E and used it on many trips just buying a new sim card each time if they had expired. The quality is terrible; my husband is getting deaf and he found he could not use them after a time. He has an unlocked I phone and we have a plan in the US that supposedly includes inexpensive international roaming and are going with that this time; this phone feeds into his hearing aids and so it is easier for him to use. Since our fall trip takes us into 4 countries, we are going to give this a try this trip. I'll report back on the Iphone/Tmobile experience.

I find the sound quality of the cheap phones also terrible but at least I can hear them. I would never rent a phone since I know a couple of people who got hit with terrifying bills that they claimed were scams; one was getting billed for calls after she had left the country and they were automatically drafted. If you buy one, it is yours and they are easy to top up.