"insistence upon legitimacy," 1849, from French légitimisme (1834); see legitimate (adj.) + -ism. In 19c. especially with reference to French or Spanish politics and conservative adherence to "legitimate" claimants to the throne.
mid-15c., "lawfully begotten, born of parents legally married," from past participle of Old French legitimer and directly from Medieval Latin legitimatus, past participle of legitimare "make lawful, declare to be lawful," from Latin legitimus "lawful," originally "fixed by law, in line with the law," from lex (genitive legis) "law" (see legal). Transferred sense of "genuine, real" is attested from 1550s. Related: Legitimately; legitimateness. The older adjective in English was legitime "lawful, of legitimate birth" (late 14c.), from Old French legitime, from Latin legitimus.
word-forming element making nouns implying a practice, system, doctrine, etc., from French -isme or directly from Latin -isma, -ismus (source also of Italian, Spanish -ismo, Dutch, German -ismus), from Greek -ismos, noun ending signifying the practice or teaching of a thing, from the stem of verbs in -izein, a verb-forming element denoting the doing of the noun or adjective to which it is attached. For distinction of use, see -ity. The related Greek suffix -isma(t)- affects some forms.
<a href="https://www.etymonline.com/word/legitimism">Etymology of legitimism by etymonline</a>
Harper, D. (n.d.). Etymology of legitimism. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/legitimism