If the answer is simply that the producers liked Stewart as an actor, that's fine. But it's kind of bugging me. Picard plays up his Frenchness. Why not a hire an equally good actor with a) no accent or b) a French accent?
There's no such thing, for the record.
I find it funny that people don't understand that, too.
I wonder what is the accent that the OP calls "no accent"? Standard American?
There's absolurely no reason why a person whose first language is not English but
who has learned English perfectly would speak with a foreign accent. In fact, it would be quite insulting to suggest that no Frenchman could ever master English so well that no trace of French accent could be heard in his speech.
When a person is learning English as a second language, they will naturally adopt one existing accent or another, or a mix of them if they are exposed to more than one. If they have learned English by living among people who speak the language, they will emulate the accent of the environment. If they have learned it in school, they will most likely be taught to speak in one or two accents that are accepted in schools as "standard English". Until very recently, this was always only RP (Received Pronounciation/Queen's English/Oxford English), the 'standard' version of British English. Nowadays its status in schools and universities is shared by standard American English, called General American. Students are rarely taught to speak in any other accents, though they may be taught to be able to differentiate between them and to understand them. (It may be different if one of your teachers at the university is a native speaker with a specific regional accent, but I don't know how often this happens.) Finally, if you don't live in a country where English is the first language, but you are exposed to the English language all the time - via film, TV (in the countries that use subtitles instead of dubbing), music, cable and TV channels, etc., you might also end up speaking in a mix of different accents. I suspect that this is my case, my English accent is probably a mix of different American and British accents I've been exposed to, although mostly the 'standard' ones that I was taught at the university.
We don't know what the standard accents will be in 24th century, but as someone who speaks English as a second language exceptionally well, it is not aty all surprising, and actually quite likely he would speak in one of the standard accents of the English language. So why not the standard British accent? Would you be complaining if he had an American accent?