The 32-year-old defender had surgery to remove a tumour on his liver in March 2011, returning to action after seven weeks to take part in the last six matches of last season, including the 3-1 victory against Manchester United in the Champions League final.
There is not a date set for Abidal's return yet, but it is possible that he may not feature at the European Championships.
"In moments like this, there is not much to say," Blanc told the French Football Federation's (FFF) website. "This is sad news for Eric.
"This is also sad news for the technical staff and for me, the coach. This goes beyond football."
The 46-year-old also sent a message of support to Abidal and refused to say whether he is making plans without the Barca defender for Poland and Ukraine.
"I hope he will once again demonstrate all his mental strength, which will allow him to overcome this difficult period," Blanc added.
"I hope to discuss the situation with him verbally. What I can say now is that his availability for Euro 2012 is not what concerns me.
"Today, I am thinking about the man and then we will make choices if we have to."
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