Why spell it connoisseur?
You’ve basically answered your own question here.
The French word has been spelt connaître for close to two centuries.
Connoisseur was borrowed into the English language some time around three centuries ago, when it was spelt that way in French.
The fact that French has changed the spelling of the French since does not mean that English (who is, generally speaking, very conservative about changing spellings) will change the spelling of the English word.
Similarly, around the same time as connoisseur was borrowed, the verb itself was also borrowed as reconnoitre (now spelt reconnoiter in American English—one of the places where English has changed spellings, though in a more or less systematic fashion). That word is pronounced with the stress on the ‹oi›, which is pronounced as /oi/. ‘Updating’ the spelling to the current French spelling would make the spelling less representative of the pronunciation of the word, which would be silly. When English spelling does get updated, at least it’s usually to make it more representative of pronunciation.
French has undergone a sound change, whereby the older diphthong /oi/ split into two different forms: one was /wa/, the other /ai/, which was later monophthongised into /ɛ/. The first of these is still spelt ‹oi› (as in François), whereas the latter is now spelt ‹ai› (as in Français). But this change mainly happened at a stage where many words had already entered the English language, and thus it was not reflected in those English words.
Some words were borrowed later on, though, and in those words, the English pronunciation/spelling match that of Modern French: in je ne sais quoi, the last word is pronounced /kwa/ as in Modern French; and in reconnaissance (which was borrowed about a century later than reconnoitre and connoisseur), the spelling in French had already changed, so the English form matches the Modern French form.
Why use the word at all?
Your second question seems to be doing the same as your first question: implicitly assuming that French does not change. This is of course not so.
If you look in a French dictionary, the word connaisseur is indeed there. My Hachette Dictionnaire de la Langue Française, for example, defines it very simply:
connaisseur, euse a, n Expert en une chose.
The fact that this is not a word French people tend to use nowadays doesn’t mean they didn’t 300 years ago when it was borrowed into English. The fact that it was borrowed at all suggests that they did, in fact.
Whether a word stops being used and fades into obscurity or maintains its popularity in any given language is completely unpredictable. The fact that this word has all but vanished from colloquial French, but managed to stay alive and kicking in English, is quite random and could not have been predicted; but once the word was there in English, there’s no reason the English should stop using it just because the French did.