Royal hopes to get majority backing from the estimated seven million voters who supported centrist candidate Francois Bayrou, out of the race after placing third in the first round earlier this month.
In a French television interview Monday Royal accused Sarkozy of peddling in brutality and violence in a major speech he delivered Sunday.
Sarkozy criticized the violent student protest movement that shook France in 1968, a movement many in the French left have held up as a defining moment of their political cause.
Sarkozy topped the opening round of the elections garnering more than 31 percent of the vote. Royal came in second with nearly 26 percent. - VOA News