Where to get help for unrooted phone that won't boot after switching from original carrier?
T-mobile (toll free): 1-877-746-0909. 
T-mobile (direct): 1-505-998-3793.

I called T-mobile, and they said I had to contact the manufacturer.

LG (toll free, US): 1-800-793-8896

They also have a french version of the website, which you will go to by default when accessing lg.com if you are on a French ip.  You can otherwise access it by going to lg.com/fr . Conversely, you can go to the US version of the site via lg.com/us .  Either version supports a live chat function and has other relevant contact information.

That answers my question of who to contact for support, but I feel it is worthwhile to now note what options I appear to have.

After talking to the US support and French support, I don't really have any options for a quick repair.

I could send it in to LG in the US, which will take them 5-7 days after they receive it, but then they will only return the phone to an address within the US.  Taking into account the mailing times, the cost to get the phone there, and the cost for someone to send it back to me, then this gets a bit costly and slow.

They won't repair American phones outside of the US.  And to make things worse, my particular model isn't even available in France.

So the only reasonably quick solution to needing a phone is to buy a phone here in France.  What to do with my existing phone is a problem that's outside the scope of the question I initially asked, so I leave it at that.