In my experience, the French are extremely picky namers, so it sounds like you have your work cut out for you! 
My best friend was French, and I felt like I missed much more often than I hit when I was trying to help her name her triplets. I really love Édith and Charlotte from his list, but I really dislike the French pronunciation of Édith. I want to like it, because I love French names, but certain ones I just don’t like the French pronunciation at all. 
I’m the same way with Geneviève (zhahn-vee-ev) and Adélaïde (add-eh-lah-EED). A few ideas:
Léonie (I personally prefer the more German (?) Leona, but Léonie’s very sweet)
Amélie (I’m personally really biased here, as it was my best friend’s name, but Amélie/Amelie is really catching on in English speaking countries, so I think it has really great cross-over appeal here. But I think it is a wee bit on the dated side in France, so he might not be thrilled about that? Same with Aurélie)
Odette/Odile (two of my very favorite French names!)
Cécile
Hélène (ay-LEN in French)
Thérèse (tay-REZ in French, I think. I think it is a great way to get to Tess/Tessa, if you like)
Agnès (maybe not the best in English, but it’s so darling in French! It’s pronounced ahn-YESS, and I think Anya or Annie would be a really adorable nn for it! I think something like Agnès Ophélie would be really adorable, too)
Ophélie
Olivie (I think this is so lilting and sweet. OL-ih-vee/OL-ee-vee. But in English it sort of transforms into Olla-vee, which I think is so cute!)
Fleur
Lise (I think Lisette and Élise are to die for, as well, but I’m not sure how a French person would see them? I feel like they’re more dated than in-style)
Élodie (I mainly love the versatility of this! She could be Ella, Ellie, Lola, Liddy, Lottie… My car is an Élodie Claire, and I call her Liddy. Mainly because she’s temperamental like Lydia Bennet. :))
Émilie (I think Emily’s sort of tired in most English speaking countries, but as soon as I see it in French, I swoon! I think Émilie is fantastic. I love saying it in French, too. ay-mee-lee. ay-mee-lee. ay-mee-lee. So sweet. But if he didn’t like Emmeline/Emeline, he might not like this?)
Isabelle
Arianne/Ariane
Camille (very in-style and popular in France, maybe even trendy. I think it’s much more beautiful with a French accent, though: cah-MEE! :))
Rosalie
Coralie
Gisèle
Aurore (another one of my favorite French girls’ names; it’s so lilting in a French accent, and still has all the great nns of Aurora–Ari/Ara/Aura, Rora, Rory, etc.! I feel like it’d be not-so-well received in an English speaking country, though, as it’d tend to be said like “a roar”.)
Mathilde
Angélique
Veronique
Frédérique (Edie could be a pretty adorable nn for this!)
Anne-Sophie
Anne-Claire
Violette (vee-oh-LET)
Adèle/Adelie
Anne-Laure
Good luck!
ETA: I would avoid suggesting Cosette, Eulalie, and Soleil (or, really, any word name in French. Would we name our daughter Sun? No, not really, and neither would the French. And it’s even worse for them because “soleil” is masculine.). Eulalie sounds pretty in English (yoo-lay-lee), but in French, it’s ehoo (sort of like eh and then oo rolled all together in one sound. It’s hard to describe)-lah-lee, and most French seem put off by that because the first syllable sounds a lot like how they say “uh”. They don’t like a name to start out that way, because it sort of seems to indicate to them that it’s an unattractive and unconfident sound. Most people I’ve talked to who are either French or have strong French backgrounds all have this reaction to it. And Cosette they just find especially childish and cutesy, and think it’s rather ridiculous to use on an actual person, as an actual name. A lot of the names popular there right now–like Emma, Lilou, Manon, Lola, Zoé, Chloé, etc. (not those exactly, but I imagine it’s those types of names?)–French people don’t seem to be too excited about, either, because they all feel very cutesy and trendy to them.
And if you already know all this, I apologize–I’m not trying to talk down to you or anything; I just have extensive knowledge from helping my best friend out. Good luck!
), [name_f]Sandrine[/name_f], [name_f]Emmeline[/name_f]
(And others)