Every pet entering France from the EU needs an electronic microchip, and it has to be implanted before, or at the same time as, the rabies vaccination. A vaccine given before the chip is in place doesn't count under EU rules, and has to be repeated once the chip is implanted, which restarts the clock on the waiting period.
The rabies vaccine itself can't be given until the animal is at least 12 weeks old — that's the minimum age the vaccine is licensed for across the EU, France included. If this is the pet's first rabies vaccination, or a previous one has lapsed, you then have to wait at least 21 days after that vaccination before travelling. France is one of the EU countries that does not allow any exception to this for very young pets; a handful of other EU countries permit limited under-age travel in narrow circumstances, but France requires the full 12-week minimum with no shortcut.
Keep the microchip number, the vaccination date, and the passport entry consistent — ask your vet to scan and confirm the chip at every appointment. A mismatch between the chip number and the paperwork is one of the more common, entirely avoidable reasons pets get held up at a border check.