In France, driver's licences issued by non-EEA countries are only valid if they are written in French, or accompanied by a notarized translation or an International Driving Permit.
Quoting from the official information page from the French authorities:
Vous pouvez conduire temporairement en France avec votre permis
délivré par un pays extérieur à l'Espace économique européen (EEE),
sous certaines conditions. Les règles qui vous sont applicables
varient suivant votre situation : court séjour, installation ou
poursuites d'études en France.
Si vous venez en France pour un court séjour (pour des vacances par
exemple), vous pouvez conduire avec votre permis. Il doit être valide
et être rédigé en français ou accompagné de sa traduction ou d'un
You can under certain conditions drive in France with a driver's
licence issued by a non-EEA country. ...
If you are in France for a short period (e.g. for holidays), you are
allowed to drive with your foreign licence. It must written in French
or accompanied by a translation or an International Driving Permit.
In the USA, International Driving Permits are issued by AAA or AATA for a US$ 20 fee (plus postage if you apply by mail instead of going to a local office).
I didn't think it should be necessary to go into details about the consequences for violating these regulations, but since both Greg Hewgill and Savannah seem to indicate and believe that an IDP or a translation is not necessary because they were able to rent cars in France with only their US or NZ licence, here some further information:
The rental company is beyond all doubt entitled to refuse handing out a car to you if you can only present a foreign licence, which for itself is not valid in France. For exmaple, the wording in Sixt's terms and conditions is that at pickup, the driver must 'submit a driving licence that is valid in France'. Note, that the terms do nowhere obligate Sixt to actually verify that you have presented a licence, which is valid in France. Other rental companies are very likely to operate with similar conditions.
Any insurance (liability insurance is mandatory in France) of the rental car is likely void. To stay with Sixt, they clearly state in their terms and conditions, that the insurance policies do not apply if the driver, at the time of the accident, does not have a valid driver's licence.
I was not able to find any specifics on the legal consequences of driving with an unrecognized foreign licence in France. Penalties for severe traffic violations are unusually high in France and driving without a licence carries for example a one year imprisonment and a 15,000€ fine. The page I previously linked to has a very clear warning: 'Si vous conduisez avec un permis étranger non valable en France, vous risquez une peine de prison, une amende et la confiscation de votre véhicule.' or in English: 'If you drive with a foreign licence, which is not valid in France, you risk imprisonment, a fine and confiscation of the vehicle.' From this statement, I would assume that driving with an unrecognized foreign licence carries the same penalty as driving without a licence at all.