A French investment group reached an agreement with the U.S. Justice Department that could pave the way for the group to take control of beleaguered online poker operator Full Tilt Poker, an attorney for the investor group said Thursday.

The agreement provides that U.S. poker players—who had $150 million credited to their player accounts but never paid to them by Full Tilt Poker—would seek compensation through the Justice Department. However, it doesn't guarantee they will get that money back, according to people familiar...