Does Europe now have a salary cap at the club level (unlike USA's salary cap at league level)?

Salary caps don't prevent football being "big business". All what they do is redistributing the money from the players into the pockets of the owners.
What you need to stop the slide of football into grotesque commercialization (the worst example of which are US sports) is something like the 50+1 rule in Germany, where the fans are the owners of the clubs.