With a valid ID card, you have more than enough to enter France. Since both countries are EU members and part of the Schengen area, there are no border controls as such, so nobody's going to ask you for any additional documentation when crossing. What really matters is that your ID card is in good condition - no tears, damaged pages, or illegible information - because officials can reject it if it's too worn, even if it's technically still valid.
My partner traveled to Paris a couple of years ago without a passport and without the slightest problem; it was so straightforward that we barely noticed she was entering another country. The ID card is the standard travel document within the EU, so there's nothing weird or complicated about it. The only thing I'd recommend is making a photocopy or keeping a digital photo just in case, not because you'll need it at the border, but if you lose the original during your trip and need an ID at a police station or something like that. For hotels, museums, and restaurants, your ID card is more than sufficient.