The parliament approved the measure last week. The bill now goes to the Senate.
The Turkish resentment is so strong, says the International Herald Tribune, it has dampened enthusiasm over the awarding of the Nobel Prize for Literature to Turkish novelist Orhan Pamuk.
Pamuk himself had gone on trial before the case was dismissed on charges of "insulting Turkishness" for reportedly saying 1 million Armenians died in Turkey during World War I.
Turkey accepts many Armenians died during the collapse of the Ottoman Empire but rejects the genocide accusation.
The Nobel award comes at a time when most Turks would rather forget the Armenian killings. Turkey is also currently involved in delicate negotiations over its membership in the European Union, for which there is already much opposition in France.
"The EU wants any excuse to keep out Muslim Turkey and the Armenia issue is just the latest example," a social worker who took part in a weekend protest in Istanbul against the French bill told the Herald Tribune.