Debit card for a teen in France

You don't say where you're based. If you're based within the EU some of my comments may not apply to you.
Not everywhere accepts cards and some places only accept card payment over a certain limit. Your son will need cash as well as a card. Make sure he has some euro in hand before he leaves (I'd suggest 100 euro) so he has time to settle in before he needs to use an ATM. Check with his penpal's family where the nearest ATM is...if involves a long-ish journey it would be better to send him with a few more euro in cash.
If you're based in the United Kingdom or the Republic of Ireland (and maybe other EU countries) imo it would be much better to get your son a currency card rather than a simple debit card. Currency cards work the same as debit cards (with chip & PIN), with either a Mastercard or Visa logo. You pre-load them with e.g. euro and they can quickly and easily be topped-up online if necessary. The big advantage is that you don't pay any currency exchange fees (except when you load other card) or bank charges when you withdraw cash or make a payment, which you most certainly will with an ordinary bank debit card. 
In the UK (maybe elsewhere) two of the longest-established and thoroughly reliable currency cards are Caxton and Fairfx but there are lots of other options. With the two I've mentioned the only charge levied is when the card is initially loaded (or if it's used in the home country, which of course it wouldn't be). If you can I'd strongly recommend getting such a currency card but do check out their charges before you decide which one is best for your son.
If you still prefer a debit card:
1. Don't just ask your bank. They will, of course and inevitably, advise one of their own cards. 
2. Mastercard and Visa are the most widely-accepted cards in France (and in Europe...the continent...in general). It's best if you get a card with one of those logos and avoid Amex and other cards which are not so widely-accepted.
3. To pay for anything and to get euro from ATMs a debit card must have a chip and PIN.  Just signing is highly unlikely to be acceptable, especially when the card is being used by a child.
4. Assuming your home base does not use euro, make sure you know, and explain to your son, exactly what your card provider will charge for a) making a payment in foreign currency and b) the exchange rate for your currency to euro. Both charges will be applied to every transaction so its important your son understands that each time he uses the card he will be using up more of the debit card funds than just the simple equivalent amount in euro.

I'm guessing you are in the US, because you said your son was flying abroad.  If not, you should probably disregard my answer.  I think it's great your son is traveling by himself to Bordeaux.  It's a beautiful city, and I'm sure he will have a great time.
I think the easiest thing to do would be to get your son a debit card on your checking account, assuming you have a US checking account with a major bank.  If it is a major bank, it will probably be a Visa or Mastercard, which it used almost everywhere.  He will get a card and a pin (has to be only 4 numbers last I looked), and he can use it at many, many ATM's in Bordeaux and all over Europe.  The money would be drawn out of your checking account, and you can see what he takes out if you have online banking.  If he is traveling to Europe by himself, he must be a very responsible young man, but there are limits on what he can withdraw at one time if you have any worries about that.  Ask about it at your bank if you have any questions.