The president can fire the FBI Director for cause. It's pretty easy to come up with causes.
Maybe he can, maybe he can’t.
I fond the following in this, it is not specific under what circumstances the President can or cannot fire a FBI director.
https://www.yahoo.com/news/independent-fbi-director-230807517—politics.html
The director of the FBI serves at the pleasure of the president...he can be dismissed if Trump doesn’t like the tie he is wearing.
“Cause” can be as simple as, “I want my own team”.