Hello people, I'm French, not a Leicester City fan - sorry- but thanks to Puel I'm following your team.
Some informations from France (I mainly follow Ligue 1 and I spoke with Puel in two occasions):
1. Puel is a very calm person. Even if he were fluent in english, he would be very calm and quiet. Some people hate him for that as football today is more about idiocy than football. Some of your fans will hate him for that. It's quite normal in our era. That's how he speaks in French:
2. Puel is passionate. Truly passionate. He doesn't care much about the media. Have a look at him when someone from your team scores and you will understand how he really is.
3. Puel loves discipline. He is disciplined towards himself and wants discipline from players. He built his own career around discipline (when he was a player at Monaco, it was his main quality). It's not only about yelling against players. Puel creates structures inside the club to make the players more disciplined and professional.
4. Puel can show a lot of love toward a player (it was the case with Ben Arfa and will certainly be the case with Mahrez). Yet, there are no free-pass for those players.
5. Puel is one of most respected French technician. Technicians from the French Federation of Football know he is one of the best technician in France right now. Actually, if he was not that quiet, he could have been the French national coach for the World Cup (that's what people say in football circles... sadly, not in the media).
6. Puel is known in France to take an average team with some potential and make it a lot better: Lille/ Nice/ Monaco (even if Monaco was a fairly big club at the time).
7. In big clubs he can struggle. With Lyon he struggled a lot. He spent 124 million euros in two transfer windows (which was a lot at the time) and still struggled. Lyon was like the PSG of today (in France) and he couldn't win the league. He is hated in Lyon for that. That semi in UCL was not that big for Lyon supporters.
8. Puel is stubborn. More than Wenger (I think it's natural for you to compare with another French coach, so... I'm doing it). If the board doesn't follow him, he can stop at the end of the season (he never abandons his teams like that, which I think is a good point).
9. Puel is a very hard worker. He dedicates his free time to football.
10. Puel is very demanding towards himself. It's not obvious like that, but he is physically a beast. You will often see him running with the players for kilometers or even playing football with them. He doesn't like being a spectator during the trainings.
11. Puel doesn't care about age. He will put the best player on the pitch. If this player is 16 years old, so be it. He gives many chances to young players.
12. Puel does like fresh players. Turn-over is very important for him (it's even more important in England because of the Boxing Day).
13. Puel loves trying new players. He can buy a lot of small players and make them good (or good enough to play league games). He takes some calculated risks and can sometimes win (or lose).
14. In terms of tactics, Puel likes possession. He can also do a kind of Catenaccio à la Française (same as Raniery), when he doesn't have the quality in his team.
I think he is the best French coach right now (above Zidane as Zidane is managing egos). A lot of French people won't aknowledge it. I'm a PSG fan since decades. I've never been a fan of his teams. Still, I can aknowledge the quality he brings to his teams. I think Puel is the best French coach.
P.S: Sorry for my poor english. I'm doing my best.