Here's the listing in Old English Translator for offrian:
offrian | weak class 2
Verbs in Old English often form their infinitive with -an, an inflection that degraded to -en or -e in Middle English and disappeared in Modern English. More specifically, Offrian is a weak verb, class 2, which often form their infinitives with -ian (Wikibooks: Old English/Verbs).
So -ian is grammatically necessary for forming the infinitive of a verb coming from another language, just like we would add to to form the infinitive of a newly-formed verb, irrespective of what the prior language did.
As for the Old French word offrir, it didn't replace the older usage but rather reinforced it, since the French word had accrued a few additional meanings that the Latin usage had lacked a few hundred years before. See below in the etymological description for "offer, v." in the Oxford English Dictionary:
Cognates with similar infinitives
Cognate with Old Frisian offria , offaria , Middle Dutch offeren (Dutch offeren ), Old Saxon offrōn , Old High German offrōn , Old Icelandic offra , Old Swedish offra , (Swedish offra ), Danish ofre ,
Originally from Latin
all in early use chiefly in religious context < post-classical Latin
offerre to offer to God, offer sacrifice, devote (Vulgate), specific
use of classical Latin offerre to bring before, present, offer, put
oneself forward, volunteer, present itself, occur, inflict < ob- ob-
prefix + ferre to carry, bear (see bear v.1).
Reinforced (and not replaced) by Old French
Subsequently reinforced and influenced semantically by Old French
offrir to put something at someone's disposal (early 12th cent.), to
give something to God as an offering, to make a sacrifice (c1140), to
give something as a present (c1170) and its etymon classical Latin
offerre. Compare Old Occitan offrir , ofrir (c1150), Occitan ofrir ,
Spanish ofrecer (1245; 1229 as oferecer , offerecer , 1246 as ofrir ),
Catalan oferir (late 13th cent.; also oferre , ofrir ), Italian
offrire (1313–19 as offerire ). Compare offering n.