Because you have been issued a new passport, your previous passport is no longer valid. When your consulate issues you a new passport, they should do something to the old passport to indicate this:
- keep it and not return it to you
- clip a corner of the cover
- punch holes in it
- stamp it as "invalid" somewhere
- give you a "cancelled" sticker to put on the old passport
Always use your newest passport to enter any country. It may be worthwhile to carry your old passport until its original expiration date, in case the question ever comes up of some document linking to a passport number.
A second valid passport may be issued under some circumstances. However, there is generally a special application process for this, and you would probably know whether you had done this. In the case of France:
En principe, vous ne pouvez pas avoir plusieurs passeports français. Toutefois, un second passeport peut exceptionnellement être délivré dans 2 situations : si votre passeport est immobilisé pendant une période de voyage ou si le passeport risque de faire apparaître des destinations incompatibles. ... Attention: la délivrance d'un second passeport n'est pas un droit, mais une faculté et c'est l'administration qui fixe ses critères d'attribution.
In general, you cannot have multiple French passports. However, in rare cases a second passport can be obtained in 2 situations: if your passport is unavailable during a period of travel [e.g. being held by a consulate for a different visa–ed.], or if the passport will show incompatible destinations [e.g. Israel & Iran—ed.] Note: obtaining a second passport is not a right, but a privilege and the administration sets the criteria for granting it.