There are several reasons. The first thing to note here is that the set of items belonging to each grammatical category ('gender' hereafter) in, for example Old French and Old English, are not necessarily aligned. OE cu ('cow', 'ox') and OF boeuf ('cow', 'beef') both derive from the same PIE root gwou, yet cu is feminine and boeuf is masculine. OE wifmann/wimman ('woman') is a masculine noun - but French femme is feminine.

Therefore there is no reason the influx of loans from another language should cause or promote having a gendered difference for its own sake in the target language. Not only will the sets not align (in addition to the above, consider that OF had two genders and OE had three), but gender may operate in the language according to completely different principles.

At this point let me just point out that the term gender has done the student of linguistics no service. What we're really talking about are more often referred to as grammatical categories. Turkish has none. Italian has two. Russian has three. Swahili has 18. The fact that in so many derivatives of PIE (Proto-Indo-European), there has been some semantic association with masculinity and femininity is entirely coincidental. It isn't even the case that all languages with two genders have to reflect biological sex. Many use an animate-inanimate distinction (Danish), or rational-irrational (Dravidian); Hawaiian gender reflects alienability and inalienability. It's a fact sometimes obscured by what is today very charged language. There's nothing necessary about a language using gender at all, and many languages don't. Context is sufficient to determine the sex of the referent, where humans are concerned. Nor is English the ne plus ultra of this ability; for example it lacks a gender distinction in second person pronouns, where for example Arabic has such a distinction. It's all quite arbitrary and is more often incidental to the reasons languages change.

In the case of OE, gender was assigned, at least originally, on a morphological and syntactic basis, rather than either a strictly phonetic (like Italian) or a semantic one (like Modern English). Some a-stem or o-stem nouns may have a phonetic clue in some forms, but for most nouns, there was none. A strong noun ending in a consonant could easily belong to any gender. For a large group of nouns, derivational endings such as -lac, -et, -dom, -oð, -ere, -scipe, -end, -had, -wist, and a couple dozen others were all that singled out a nominal (in isolation) as masculine, feminine, or neuter. There is evidence that some of these, whether productive or frozen, once had a semantic relationship with their grammatical categories, in PIE and maybe in Proto-Germanic, but by the time of OE, this relationship was largely obscured. This means that in isolation, gender was meaningless to an OE speaker. It could only be communicated through information coming from outside the NP, either an adjective agreeing with it, or a pronominal antcedent in another clause.

These are prime conditions for gender fluidity, and in fact there were OE nominals that have as many attestations in one gender as another. sæ ('sea'), sæl ('time'), hearg ('temple') were acceptably either masculine or feminine, as are many Latin calques borrowed prior to Middle English.

There is ample evidence OE gradually began to shift toward a semantic usage of gender, particularly where animacy or agency was concerned, as well as specificity. Referents described as patients (rather than agents) could receive neuter pronouns despite being assigned either masculine or feminine gender. Likewise referents denoting a lack of specificity, such as collectables. Hardlined gender could re-assert itself when the discussion revealed the noun or a specific member of the group noun.

All that I've mentioned was the case before 1066. If the OE three-gender system were dinosaurs, 1066 is the K/T boundary, and the Norman conquest is the asteroid. Okay, not quite, because it merely began a slow process that did not ramp up until the 1300s, when the bulk of French loans were made, but I like this analogy because there's been some evidence dinosaur populations, too, were already in decline at the time of the event, and it's not every day you can talk about dinos and OE nominal syncretism in the same post, so...I have no regrets.

A few centuries later and you have a massive influx of (Old) French vocabulary. Just like OE's attempts to gender Latin loanwords in the past, these new words are being assigned gender haphazardly and inconsistently. And it is not just the lexicon being affected. Shifts in pronunciation, especially from a vowel system of 'long and short' to one of 'tense and lax', further reduce the vowels in suffixes to schwas. Word-final -a, -u, -e, all become -e; -an, -on, -un, -um all become -en. Declensions are simplified; nominative and accusative are merged, and all cases become identical in the plural. Suffixes on nouns and verbs are losing their functional load, and syntax (word order) is picking up that load. By 1400, final -e on nominals was no longer pronounced in the majority of England.

With nominal and adjectival endings fully gone, except in the genitive (but that was a declensional distinction at this point and not a gendered one), there were few other places a speaker could acquire feedback about a noun's gender - really just determiners (demonstratives, pronouns). This will soon change, as þe (late OE masculine and feminine demonstrative 'that') came to be an article used for all genders - modern the. The late OE neuter demonstrative þæt remained a demonstrative, modern 'that'.

So now most determiners are useless for signaling gender. All that's left is the pronouns. But, without the noun (or adjective, or article) to agree with it morphologically or phonetically, there was neither much way to determine the gender of a noun in language acquisition (children, we're always talking about children here), nor was there any longer any usefulness from such limited (and arbitrary) agreement. The third person pronouns were free to complete the shift from syntactic > semantic function they had started centuries ago. And so unspecific items were neuter ('it'), female persons and animals were feminine ('her'), and male ones were masculine ('him').

One might ask, why OE was not thrown into this kind of upheaval by the earlier Scandinavian invasions as it was by the Norman one. Some people, like Charles Barber, think it was, and that Scandinavian loans initiated some of the gender instability I've mentioned here. Either way, there are clear differences. Scandi loans from the Danelaw lacked the prestige factor of a Norman-controlled court in London. The gender of Scandi loans more often approximated the gender of the OE counterpart, compared with French. The phonology of the Scandi loans was also closer. And finally the amount borrowed was simply not as extensive, and the period of bilingualism not as long or as trenchant.

Sociolinguists have likened the situation in England in the period following the conquest to that found in the origin of creole and pidgin languages. That is not to say Modern English is a creole, but it would fall somewhere on a creole-non-creole continuum. In such languages, borne out of conditions of occupation, we invariably find morphological leveling, a favoring of syntax-driven expression over morphology, a favoring of semantic-driven morphology that remains, and a lexicon that demonstrates prestige differences (French animal words all coming to mean the meat of that animal, for example: 'cow', but 'beef' / boeuf). There is much twinning in this regard between Modern English, and Modern Persian. Persian, too, saw an extended period of influence from Arabic, during which it lost its grammatical gender, its simple verbs, many moods and tenses, and where synonyms exist, prefers Arabic for technical, legal, and academic nuance.

Some sources:

Baker, Peter S. Introduction to Old English. Wiley-Blackwell, 2002.

Barber, Charles. The English Language. Cambridge University Press, 1993.

Buck, Carl D. A Dictionary of Selected Synonyms in the Principal Indo-European Languages. University of Chicago Press, 1988.

Hasenfratz, R. and T. Jambeck. Reading Old English. West Virginia University Press, 2011.

Vezzosi, Letizia. "Gender assignment in Old English." English Historical Linguistics. Bergamo, 2006.

if i may add a side question?

what would the reason for why the language dropped the gendered pronouns be? is there a logical reason or hidden value to not having gendered objects?