I personally would prefer to read the second option. As a reader, my instinct is to not read huge amounts of Italics text in other languages (unless I think I can try to mentally translate it), so it might confuse me to see that much English in Italics, and I'd prefer that large chunks of Italics be avoided as much as possible.

I think it makes perfect sense to occasionally do your "He switched to French..." or "He continued in English," and then assume if you don't mention it again that they're still speaking in French, particularly if they're in France. :)