I've long thought Favre would be a good choice for next England manager. He's comfortable with a 4-4-2 and his sides defend well. I could see him making England competent in a tournament, back to the usual quarter final defeats since they don't have the talent they did back under Sven.
He probably could do the job well, but at the same time I'm not sure he'd be at his best in that setting.
Favre works on details a lot (he's really pedantic) and some things he focuses on are things English players may not be too familiar with. So in a NT setting there may not be enough time to properly implement his ideas. But despite his perfectionist nature, he has also shown the ability to improvise with what he is given, so who knows?
Don't want to say it can't work out, I just think some aspects of his approach work best when he's a club coach who trains with his players a lot. He could be great for Arsenal, I reckon.