The news is a blow to the French champions, who have had a poor start to the season.
Ait-Fana scored a crucial goal for Montpellier in their last Champions League game, where they picked up their first ever point in the competition against Schalke.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.