If passed, the law would allow UK and other overseas firms to offer sports betting and poker in France. Plans to open up and regulate betting in France were announced in March.
This was in response to the growing number of illegal gambling sites accessible to the French, and to pressure from the European Commission to reform gambling markets.
Currently, betting in France is restricted to Groupe Francaise des Jeux, which runs the state lottery, and Pari Mutuel Urbain, which offers gambling on horse racing.
Should the restrictions be relaxed, there "is a massive potential market for any firm," Paddy Power from the Paddy Power betting firm told the BBC. However, he said that the bill was just the first step in a long political process to open up gambling in France.