I thought this would surely be an idiom. Will "His bark is worse than his bite" be accepted in the future?
The English idiom refers to people. Is the French idiom applicable to people or dogs or...?
It is idiomatic for people; people who are all threats and bluster don't actually act on it. Now whether that's true or not is another matter...
if it was "elle" instead of "il" would it have been "forte" instead of "fort" ?
No, here fort is used as an adverb, not an adjective (loudly=fort) and adverbs are invariable, they don't form agreements.
Secondly, even if it were an adjective, you would only make the noun/adjective agreement when using the verb "être."
Il est heureux. / Elle est heureuse.
Il est grand. / Elle est grande.
Really!? This is wrong because I put the adverb before the verb, which is perfectly acceptable in English? "He loudly barks but he does not bite."
I don't know the grammar rule, but here the English adverb comes right after the verb just like the French one. "He barks loudly" not "He loudly barks".