The story
- Proto-Indo-European*h₁éǵʰ
- Proto-Indo-European*h₁éǵʰs
- Proto-Italic*eks
- Latinex
- Latinex-
- Middle Frenchex-
- Middle Englishex-
- Englishex-der.?
- Englishfranchiseder.?
- Englisheffranchise
- English todayeffranchisement
From effranchise (“(archaic) to grant (someone or something) a franchise or privilege”) + -ment (suffix forming nouns meaning the actions or results of actions denoted by the verbs to which it is attached).
Etymology from Wiktionary, CC BY-SA 4.0.