I would normally use the accents. But it depends on whether you really want to pronounce them the French way or not. Otherwise don't use them.
Rémy - I like it a lot, it makes me think of the cute rat in the movie and I love that movie. Really nice name.
Pierre - this is out of fashion in France but not terribly dated. It's a classic, like Peter. It was crazy common in France in the past so not an exciting choice. I don't like it that much.
Joseph - I don't like this in any language, I find it bland and boring. Joe is kind of cute but I'd rather use Jonah. This won't really show French heritage as it is popular in so many countries.
Auguste - I don't like it in English and in French it sounds even worse, in my opinion. This is currently having a comeback in France so it is cool by French standards, I just don't like it.
Émile - I like it but in English speaking countries people might assume that this is a girls name because it looks similar to Emily.
Armand - not a fan of the sound.
Edgar - makes me think of the "Aristocats" guy, I think it sounds stuck up, sorry! I like Edmund and Edward.
Mayeul - I know that it is an old name but it looks trendy and made up. Endless pronunciation problems. I wouldn't mind because I love many Irish names but you might.
Favourites are Rémy and Émile but I''d pick Rémy it works well.
Iris - I am tired of it it seems like a name that will be super popular soon. It will be extremely hard to get people to say it the French way.
Léonie - it's fine but people will pronounce it the English way and I don't like that pronunciation.
Béatrice - nice but it will be hard to enforce the French pronunciation.
Octavie/Octavia - reminds me of an octopus. They are cool, but still...Octavia isn't particularly French and Octavie is just okay.
Adélaïde - will be extremely hard to enforce the French pronunciation. The name is okay.
Blanche - granny name but making a bit of a comeback. It is fine.
Garance - this is super old stylish in France. I find it harsh and difficult to say for English speakers.
I don't really like any of the girls names but they are all fine.
I wouldn't use a name like Béatrice in English speaking countries because people will always try to pronounce it the English way. It is harder to make people pronounce a name they know differently than choosing a new name. Same with Léonie etc. If you would pronounce them in English I wouldn't use the accents.
I love (but many of the French names I like are 80s/90s dated in France, I feel like these decades had the nicest names):
Élodie
Delphine
Amandine
Océane
Lucine
Léontine
Felicie
Camille
Maël