The Paris first instance court rejected applications for anti-arbitration injunctions in two different cases in January and March 2010.
It is important to notice that these applications were dismissed on grounds which are peculiar to arbitration law, namely the negative effect of the Kompetenz-Kompetenz principle. Under French law, this principle gives priority to arbitrators to rule on their own jurisdiction and thus prevents courts from assessing whether arbitrators have jurisdiction (subject to a very narrrow exception). It follows that it is hard to see how a French court could issue an anti-arbitration injunction, since it may not assess whether arbitrators wrongfully retained jurisdiction.
In court proceedings, there is no comparable principle (though the combination of the principle of mutual trust and of the lis pendens rule leads to a similar result when the Brussels I Regulation applies). Thus, the power of French court to issue injunctions enjoining a party from suing before a foreign court remains an open issue.