President Nicolas Sarkozy has condemned the bill saying only French and European citizens who share the "same destiny" should be allowed to vote. Currently, only French and EU citizens can vote in local elections.
However the Socialist Party wants to extend that right to non-EU citizens who have been living in France for more than five years. PM François Fillon is to urge senators on Thursday to vote against the proposal and debates in the Senate are expected to be heated.
Supporters of the far right party the National Front have planned a demonstration against the bill in front of the Senate. Several far left and green politicians are to stage another protest in favour of the bill. Green candidate Eva Joly, who is Norwegian-born, is expected to appear.
61 percent of the French support the proposal to give foreigners from outside the European Union a right to vote, a recent Le Parisien poll shows.
In 2005, Sarkozy had come out in favour of extending voting rights to non-EU citizens. This has led many commentators in France to accuse him of changing his mind to attract more hardline right-wing voters ahead of elections in 2012.
If passed by the Senate, the bill is likely to be overturned by the National Assembly, which is controlled by the rightwing UMP party.