After arriving in France from Georgia to play for Massy, aged 21 Kubriashvili moved up the leagues to the Top 14 with Montpellier.
Kubriashvili soon worked his way to becoming first choice for Toulon in 2009 and remained first choice for the following season.
In May 2013, he played as a replacement as Toulon won the 2013 Heineken Cup Final by 16–15 against Clermont Auvergne.
He joined Stade Francais in 2015, returning to MHR as a medical joker. He has played 38 times for Georgia and is contracted to Montpellier until 2018.
Following the conclusion of his contract with Montpellier, he signed a deal to join recently promoted side Grenoble ahead of the 2018/19 Top 14 season.
JW July 18
|2018 - present|
|2008 - 2013|
|2014 - 2014|
|2013 - 2015|
|2007 - 2018|
|2008 - 2019|