Sunday's first round of the election indicated that President Nicolas Sarkozy's UMP conservative party is at 45.5%, and the rival socialists hold 47%.
On top of this, Nicolas Sarkozy's popularity has declined in the recent past and he was under criticism at one stage for devoting more time to his romance with Carla Bruni than his official duties.
However, the socialists' lead is nevertheless less than had been forecast by several political analysts.
The second round run-offs take place on 16 March, and around 44 million of the voting public in France are selecting mayors and councillors in over 30,000 cities, towns and villages of the country.
Francois Fillon also added: "What is at stake today is the management of our towns, villages and provinces."
