Which player has the most goals from free kicks in professional football history?
That would be the Brazilian player Juninho. His Wikipedia article, citing three separate sources, states:
Noted for his bending free kicks, he is widely considered to be the greatest free kick-taker of all time and holds the record for the highest number of goals scored through free kicks with 75.
Google brings up multiple sources, such as this one, that credit him with 77 free-kick goals. Every article I can find, however, agrees that Juninho holds the record, regardless of what his total is.