Here is the relevant part of the discussion of party in Ernest Weekley, An Etymological Dictionary of Modern English (1921):
party. Represents both F. partie, p.p. fem. of partir, to divide, and parti, p.p. masc. Usual F. senses are partie, part, parti, party, faction, but they have become much mixed in E. Sense of friendly gathering is partly due to F. partie, game, excursion, etc. Slang sense of individual, e.g. nice old party, arises from earlier leg. sense as in guilty party, i.e. side, to be a party to, etc.
So according to Weekley, three French words were influential in the emergence of party in the sense of "friendly gathering": parti meaning "faction," partie meaning "part," and partie meaning "game or excursion."
The Oxford Dictionary of Word Histories (2002) has this:
party [Middle English] The early use of party was to refer to a body of people united in opposition to others, as well as specifically to a political group. It comes from Old French partie, based on Latin partiri 'divide into parts'. The sense 'social gathering' dates from the early 18th century.
Neither Weekley nor Oxford seems at all surprised by the historical changes that saw party in the sense of a political gathering born of opposition to something expand to include a social gathering for nonpolitical purposes and from there grow to mean also a friendly gathering where hors d'oeuvres and alcoholic beverages are consumed.