The short answer is that we don't know for sure. Sans serif is a compound formed in English between the long-used English preposition from French sans and serif, most likely invented by printers creating new typefaces.
Oxford English Dictionary, "serif, n. and adj." gives an explanation that mentions the term sanserif:
Any of the cross-strokes or finishing strokes at the end of a principal stroke of a letter. Cf. sanserif n.
Many of the early spellings (late 18th, early 19th century) are inconsistent: ceriph and surriph show up as early forms. Serif as a spelling shows up sometime in the 19th century. Also, the word is Dutch in origin: schreef means a line or a stroke.
Meanwhile, sanserif appears in the 19th century, sometimes as san-serif, sometimes sans-surryphs or sans-ceriph before the spelling stabilizes as sans serif:
A form of type without serifs: called also grotesque. Also attributive. Cf. serif n.
Context in Printing
While sans serif typefaces were already around, London printer Vincent Figgins published the first known mention of "sans-serif" in his Specimen of Printing Types. The OED lists 1830 as the first use; here is one page from the 1834 edition, via Internet Archive:
The use is jargony. The entire book has typefaces with labels referring to size (e.g., "twenty line pica," "two-line great primer") as well as form (e.g., "antique," "sans-serif," "perspective"). Figgins's jargon would soon seep into other guides. Here is Alexander Wilson, c. 1842:
By 1842, the word was already in use in debates about which font is more appropriate for the visually impaired (Statements of the Education, Employments, and Internal Arrangements, Adopted at the Asylum for the Blind, Glasgow):
Dr. Fry's alphabet is the sans-serif, of type-founders,-- plain roman capitals, merely deprived of the small strokes at their extremities.
Why would a printer combine a French-original preposition with a Dutch-original stem? We could make a few guesses. The preposition sans was already in English, and it has sometimes been used for non-French words - sans delay. It is quite possible that the people who first used it saw serif as a technical term - or even mistakenly thought it was a French one - and felt sans was more appropriate to use with serif. Also, there may be an argument from form: more words are formed from sans than from without, illustrating how open the two prepositions are to forming new words. (22 words headed by sans in the OED and 3 headed by without.) In any case, it's hard to say for sure. Word formation can be an arbitrary and idiosyncratic process.