Wait, her name is really Eugene? This isn't a typo?
I had the same reaction of surprise as you, being French myself, I can say with all certainty that this is an unambiguously masculine name, even if there are unisex names in our language, this is not one of them. There are, however, feminine variants of this name, such as Eugénie or Eugénia, but it's a rather rare name in its feminine version, often judged to be very old-fashioned, somewhat outdated and not necessarily a very beautiful name either. In junior high school, I knew a girl whose name was "Eugénie" and it was a constant source of mockery, in addition to her somewhat unattractive physique - school cruelties be damned. Funny how it reminds me of that distant past now ! x)
P.S. Don't hesitate to ask me for advice on French names and expressions.
If you want to Frenchify the names of the characters in the breakfast scene at the very beginning, after the prologue, it goes something like : "Damien" (for Damian), Zoey (this works very well, a not-so-common first name that enjoyed a resurgence in popularity some time ago), Gabriel (works for the masculine, for the feminine you have Gabrielle or Gabrièle, Gabriella with one or two "l "s for borrowing from Italian or Spanish), "Luc" (for Luke) in its French form, or possibly Lucas very close to it (Lucie in the feminine form), "Eugénie" for a more correct feminine name, although it's not a very popular one (the masculine Eugène is more frequent, although it too is a relatively rare name, though less so than its feminine versions). I strongly recommend changing "Eugène" for "Eugénie", or even opting for a more pleasant and more frequent feminine name.