Larousse, "Dictionnaire des Prénoms" (which is generally pretty reliable) lists Amantine as a diminutive of Amante and Amanthe (both feminine). And those are listed as variants of Amande and Amanda.
As for usage, the book mentions that among the feminine variants only Amanda survived to this day; or rather, reappeared in the 1970s. The other variants were used during the Middle Ages but disappeared in the 20th century at the latest.
The book is from 2009, by the way.