After playing at the 2011 World Cup, Kubriashvili lost a bit of form. Hayman became first choice again, and Kubriashvili has been the second choice since. In May 2013 he played as a replacement as Toulon won the 2013 Heineken Cup Final by 16–15 against Clermont Auvergne. In the summer of 2013, he joined the Top 14 side Stade Français.