Firm
Middle English: from Old French ferme, from Latin firmus .
wiktionary
From Italian firma(“signature”), from firmare(“to sign”), from Latin firmare(“to make firm, to confirm (by signature)”), from firmus(“firm, stable”). The contemporary sense developed in the 18th century simultaneously with German Firma(“business, name of business”). There are conflicting statements in the literature as to which of the two languages influenced which.
From Middle English ferme, from Old French ferme, from Latin firmus(“strong, steady”). Doublet of dharma.
etymonline
firm (adj.)
late 14c., ferm, "strong, steady" (of things), "permanent, enduring" (of agreements), "steadfast, steady" (of persons), "sound, well-founded" (of arguments), from Old French ferm "strong, vigorous; healthy, sound; steadfast, loyal, faithful" (12c.), from Latin firmus "strong, steadfast, enduring, stable," figuratively "constant, steadfast, trusty, faithful," from suffixed form of PIE root *dher- "to hold firmly, support." The spelling return to -i- in late 1500s was modeled on Latin. Related: Firmly; firmness.
firm (n.)
"business house," 1744, according to Barnhart from German Firma "a business, name of a business," originally "signature," from Italian firma "signature," from firmare "to sign," from Latin firmare "make firm, affirm," in Late Latin, "confirm (by signature)," from firmus "strong; stable," figuratively "constant, trusty" (see firm (adj.)).
firm (v.)
c. 1300, fermen "make firm, establish," from Old French fermer "consolidate; fasten, secure; build, set up; fortify" (12c.) or directly from Latin firmare "make firm; affirm; strengthen, fortify, sustain; establish, prove, declare," from firmus "strong, steadfast, stable" (see firm (adj.)). Intransitive use, "become firm" is from 1879; with up (adv.) from 1956. Related: Firmed; firming.