The French parliament is due to discuss the bill, proposed by the Socialist opposition, on October 12.
Turkey strongly denies charges that some 1.5 million Armenians perished at the hands of Ottoman Turks in a systematic genocide, saying large numbers of both Christian Armenians and Muslim Turks died in a partisan conflict raging at that time.
''What will you do when Turkey's prime minister goes to France and says 'there was no Armenian genocide'? Are you going to put him in prison?'' the state Anatolian news agency quoted Erdogan as telling a group of French businessmen in Istanbul.
''We expect you to expend every effort to prevent this (bill from passing),'' he told them.
''Our warnings should not be taken lightly. The seriousness of the situation must be understood,'' Erdogan added.
Turkey's Foreign Ministry and a group of Turkish lawmakers who visited Paris last week have already said the draft bill will damage bilateral economic and political ties.
Large French companies including Renault and Carrefour have large investments in Turkey, which has a fast-growing economy and is a candidate to join the European Union. Total bilateral trade amounted to nearly 10 billion dollars in 2005.
Though the conservative majority in France's parliament opposes the bill, Turkey fears many opponents will not vote against it for fear of upsetting France's 400,000-strong Armenian diaspora ahead of elections next year.
Last year, Erdogan proposed a joint commission of Turkish and Armenian historians to examine what really happened during World War One. Armenia did not accept the proposal.
Turkey began its EU entry talks last year, though is not expected to join for many years.
Recognition of the Armenian ''genocide'' is not a condition of its EU membership, though some EU politicians including French President Jacques Chirac have suggested it should be.