The contest is the first nationwide vote since Socialist leader Francois Hollande was elected as president two years ago.
It comes at a time when the centre-right UMP has been hit by a corruption probe as well as other scandals allegedly involving former president Nicolas Sarkozy.
Tensions reached a peak just ahead of the polls with Sarkozy likening the court-ordered phone tapping on him to the methods employed by East Germany's dreaded Stasi police, drawing a sharp reprimand from Hollande.
Amid the flagging fortunes of the two main parties, the National Front (FN) of Marine Le Pen is on the rise.
The far-right party founded by her father, Jean-Marie Le Pen, is fielding a record number of candidates in the municipal elections.
Marine Le Pen has voiced her confidence and the party hopes to wrest control of 10 to 15 cities.
Under France's run-off system any party which wins 10 percent of the vote goes forward to a second round.
A strong first-round showing will not necessarily translate into the FN securing control of many local authorities, and it is only contesting around one in five municipalities.
But an outcome on the lines indicated by the most recent opinion polls would nevertheless send shockwaves through French politics.
Hollande, who failed to keep his electoral pledge to rein in record joblessness by the end of last year, is the most unpopular president in recent French history.
Some 30 percent of voters have indicated they intend to punish the government for its perceived failures on key issues such as jobs, although experts play down the likely impact of recent scandals.
Marine Le Pen, who gained 17.9 percent of the vote in the 2012 presidential election, has urged voters to reject candidates from a "system that is taking French political life down the gutter."
Le Pen believes that France has lost its sovereignty to the European Union and wants to see an end to open borders across the continent and laws being made in Brussels for EU member states.
Her anti-immigration and Eurosceptic views are shared by large numbers of French voters, many of whom have been hit hard by economic austerity measures that are seen as coming from Brussels.
Ironically, the FN's high standing in the polls is expected to help the Socialists reduce their losses. By splitting the vote on the right, Le Pen's party will make it easier for the Socialists to get into more second rounds, and, in the event of run-offs against the FN, to win them.
In Paris, under the control of Socialists for 13 years, there is a historic tussle between two women candidates.
The current Socialist mayor's deputy Anne Hidalgo is fighting a challenge from the UMP's Nathalie Kosciuscko-Morizet, a former minister in Sarkozy's government.
Polls have shown the UMP and Socialists neck-and-neck in the first round but Hidalgo is expected to edge in the second round.