Praying with Muslims from other sects apart from the followers of Ahlul Bayt (AS) is allowed and recommended. Friday prayer leader has conditions including being a pious follower of Ahlul Bayt (AS). You can pray behind non Shia Shaikh and you get the reward of praying with other Muslims, but it will not be a valid Friday prayer, and you must perform your own Dhuhr prayer either before or after.
Wassalam.