Papidze began his career in France with Lyon OU before joining Nevers, which enabled him to be a JIFF player (joueurs issus des filières de formation, loosely translated as "academy-trained players").
Papidze first experienced French rugby at the age of eighteen with LOU alongside Antoine Nicoud. In 2018, he joined USON Nevers Rugby, where he spent three seasons, playing a total of 37 Pro D2 matches.[4]
During the 2021-2022 season, he participated in 19 Top 14 matches with 3 starts for Stade Rochelais.