As a former French history professor, my recommendation is:
1) Make your questions specific & focused. (I suspect you've already got this one covered.)
2) Research to identify someone with the right area of expertise to ask. You've already figured out what that is. So check the last 10 years or so of the relevant historical journals to see who's been writing on the subject--look at the articles, but also the reviews, & who's writing the reviews -- and also who wrote the recent works they're citing.
H-France is also a useful resource, & full of helpful people.
3) When you figure out who you want to ask, you can probably get their contact info from their university website/directory. If it's not publicly listed, contact their department for the info.
4) It used to be that summer was a very bad time to try to ask anything of a French historian, because summer is when French historians go to France. (Long, long hours in dusty libraries and archives mining for facts.) These days they won't be totally out of touch anymore. But be warned.
5) That said, if you ask a professional specialist an educated question about their specialty, they're generally very happy to answer if they can, and/or suggest resources & bibliography you may not know about, and/or recommend someone better placed to help you. (For instance, one of their grad students who just happens to be writing a dissertation
on your very topic.)
ETA: When you're doing web research, not only is JSTOR a great resource, but so is Google Scholar. Don't forget them!