OVH seems to be turning back on their threats. In his Twitter, Octave Klaba modestly announced that everything is OK now after an amendment 437 was added.
It is hard to take their threat seriously. It must be horribly expensive to move a huge datacentre without disrupting the service. The most they could have done is to move their headquarters, which wouldn't protect them from this law, and make all their growth outside of France, which is what pretty much all major French corporations do already anyway.
This is largely disputed: http://www.numerama.com/magazine/32806-boites-noires-le-gouv...
Black boxes are still there. Some light safeguards are added, notably approval of Prime Minister, but it still remains quite vague.