I'm not
Claire but I can tell you that according to the site Tous les prénoms the name
Fleur was used 3005 times between 1900 and 2003, mostly since the 70's but also a few times at the beginning of the 20th century.
Here are similar names and the number of times they were used in
France between 1900 and 2003:
Fleure 4
Fleurentine 6
Fleurestine 20
Fleurette 128
Fleuriane 126
Fleurianne 10
Fleurie 30 (the masculine form Fleury was used 1065 times)
Fleurina 3
Fleurine 614