I have tried reinstalling the game and it worked.
BUT: It only worked until I rebooted my PC.
Then I noticed that you don't have to reinstall the whole game but just some core files:
I went to the game folder and deleted every file except the two folders I marked in the image. Then I went to Steam and right clicked FC 25 in my game library, went to Properties, installed files and checked for issues with the files.
It will then scan for the missing files and re-download them (about 1.6 GB)
After starting the game again, the movement worked but I think it's only a temporary fix just like the whole reinstalling.
