The French suffix is from Latin -ina, fem. form of -inus, suffix used to form adjectives from nouns, and thus is identical with -ine (1).
The Latin suffix is cognate with Greek -inos/-ine/-inon, and in some modern scientific words the element is from Greek. Added to names, it meant "of or pertaining to, of the nature of" (Florentinus), and so it also was commonly used in forming Roman proper names, originally appellatives (Augustinus, Constantinus, Justinus, etc.) and its descendants in Romanic languages continued active in name-forming. The Latin fem. form, -ina, was used in forming abstracts (doctrina, medicina). Relics of the attempt to continue a distinction between Latin -ina and -inus account for the English hesitation in spelling between -in and -ine.
suffix used to form the present participles of verbs and the adjectives derived from them, from Old English present-participle suffix -ende, from PIE *-nt- (cognates: German -end, Gothic -and, Sanskrit -ant, Greek -on, Latin -ans, -ens). The vowel weakened in late Old English and the spelling with -g began 13c.-14c. among Anglo-Norman scribes who naturally confused it with -ing (1).