During parliamentary debate, socialist politician and leader of the La France Insoumise party, Jean-Luc Melenchon, introduced a motion to reject the bill which he said was “anti-republican" and “anti-Muslim."
Britain formally left the EU on January 31 but remains subject to EU laws and regulations during a transition period due to last until the end of this year.
France's emergency measures were imposed two years ago, after 130 people were killed during coordinated terror attacks in Paris.
Rights groups have criticised France's new anti-terror bill, with Human Rights Watch calling the measures a "normalisation of emergency powers."
Even if President Obama upholds his promise to veto the bill, the measure may still be signed into law if a majority two-thirds of both the US House and Senate vote to overturn.
Labour reform bill, which has been the subject of violent protests, to be debated in French parliament.
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