French word presque comes from French que, French près

Detailed word origin of presque

Dictionary entry	Language	Definition
que	French (fra)	(used with ne) only (ne ... que parses roughly as "(do[es]) not / nothing ... other than"). Links two noun phrases in apposition forming a clause without a (finite) verb, such that the complement acts as predicate.. Substitutes for another, previously stated conjunction.. That (introduces a noun clause and connects it to its parent clause). When, no sooner. Than (introduces a comparison) [...]
près	French (fra)	(formal, or, legal) attached to, connects a person or an organisation delegated officially to a setting. Near (a time or a place); close (to a time or a place).
presque	French (fra)	Almost.