National team star Phượng had his one-year loan contract with Incheon United FC of the Republic of Korea ended by mutual consent after just four months.
Established in 1911, Clermont Foot 63 FC have never competed in Ligue 1 and were the first professional men's team to be managed by a woman from 2014-17 under Corinne Diacre.
Currently they are managed by Pascal Gastien. The Ligue 2 season begins on July 26.
If signed, Phong, who played in Japan for Mito HollyHock in 2015, will be the second Vietnamese to play in Europe after former national team striker Le Cong Vinh turned out for Leixoes SC in Portugal in 2009.