short French lessons in Paris or Strasbourg with a focus in French for tourists

Personally - I would not spend my precious time in France in a class. Why not see about taking a class at home BEFORE you go? Hire a tutor for one on one. Check a local community college or Craig's List (meet in a public place - many libraries have suitable rooms).

Also check local universities for weekend or evening continuing-education classes. I've taken European language classes at a couple of different venues, and access to tapes (yes, this goes back quite a number of years!) to be used at home made for much faster progress than just sitting in class for a few hours once a week. So if trying to do this at home, I'd look for an arrangement that includes CDs for at-home practice.

College-based classes may not be targeted specifically at travelers (though you might find that option), but taking even one would give you some basic information in the structure of the language (gender, etc.), which can be very helpful when it comes time to form a new sentence--one that you have not previously memorized.

Looking for someone to give you some private lessons in the US is another possibility. This may not cost any more than it would in France. I took a quick look at some French language schools a few weeks ago (I'm hoping to take some private lessons myself next year, because French is not one of the languages I've studied), and the hourly rate for individual lessons was about 50 euros. That would be an "ouch", but I can't say that it's unreasonable.

There are language-exchange programs in Paris - "Franglish" and various meet-up groups - but non-English speakers seem to insist on practicing their English, instead of helping with French pronunciation, grammar, etc. I wouldn't recommend them.
If you can find someone to help you before you arrive, that would be best.

Otherwise, if you already know some basic words and phrases, you won't have to worry too much about taking your pronunciation too seriously. Waiters, salespeople, etc are quite used to hearing different accents, and they manage to figure out what people want on a daily basis. If you are polite, and give it your best shot, that's all that anybody needs.

If you're worried, you should just look up the words you plan to use to get something at the patisserie, for example - practice them out loud before you go out. You'll really be fine.

The Alliance Française on Blvd. Raspail in Paris offers courses, though you specified private classes. They do offer those but they are quite expensive. You can enroll in a class, however, for only a week. Since it's quite large, the AF has new courses beginning every week and offers six levels. I went there a long time ago, but it's still the standard-bearer for foreigners learning French. You'd be in class four hours a day.
http://www.alliancefr.org/en
Indeed, Paris time is precious, but you'd be surrounded by French language and meet a lot of others with whom to go sightseeing in the afternoon and evening. I made friends from all over the world there.

It is possible to combine a French class and a tour, it's called French'cursions. This allows to adapt to your needs (pronunciation, vocabulary for your trip, ...) while discovering a city/region. It can be very short (2 hours) or over one or a few days. A private course is also possible if you are looking for a more traditional class.
Well, this suggestion is not in Paris or Strasbourg, it is in Brittany (around Rennes, St Malo, Mont St Michel, etc), but can be worth having a look : http://visite.bretagne.free.fr/index.php/en/brittany-differently.html

Thanks everyone for the helpful suggestion :)

I used the CD lessons, Pimsleur is the name and they have several foreign language tapes/CDs. I found it was just enough to learn the basics and to be courteous with local hotels, shops, restaurants, etc.
There were 4 CDs and I listened to them several times.
I see that they are also avail. online but don't know about the cost......at the local library,they were free to check out and could be renewed as needed.
( I also did the Italian before going to Italy.)
Happy Travels.