That's quite a difficult question to answer without a little bit more guidance as finding a sweet spot when it's not too busy but not too hot or cold is very much a sweet spot.
On first reaction July-August are out for being too hot and November-Februray are out for being too cold. So I think you should check when French school holidays are and trying and find a suitable time outside of those months.
We've only been once and it was in early August - weather and crowds were great. There are certainly cooler months, but it's still not as hot as Orlando is 8 months of the year.