Relations between the two countries have been damaged since the lower house last month approved the bill which could send to jail anyone who denies the genocide.
Ankara has frozen political and military ties with France and has promised further measures if the bill is passed by the Senate or approved by President Sarkozy whose UMP party put the bill forward.
A Senate law Commission on Wednesday rejected the measure, but their vote is not expected to prevent it from becoming law.
Some ministers fear it will hurt diplomatic and trade ties with a Nato ally and major economic partner.
Foreign Minister Alain Juppé has admitted the bill is “untimely”.
On Saturday, Turkish Foreign Minister Ahmet Davutoglu repeated Ankara’s oppsition to the bill saying it goes against European values and would not help Turkish-Armenian relations.
"It is time for French intellectuals, for French senators to defend our common values, freedom of expression. These are European, French values. This is against these values," he said.
In an attempt to diffuse tension with Ankara, Sarkozy sent a conciliatory letter to Turkish Prime Minister Recep Tayyip Erdogan stressing the measure was not aimed at any state or people in particular.
France is home to an estimated 500,000 citizens of Armenian descent and the UMP has been accused of backing the law in order to pander to a key electoral demographic three months ahead of the presidential election.
Armenians say up to 1.5 million of their forebears were killed in 1915 and 1916 by the forces of Turkey's former Ottoman Empire.
Turkey disputes the figure, arguing that only 500,000 died, and denies this was genocide, ascribing the toll to fighting and starvation during World War I and accusing the Armenians of siding with Russian invaders