Valls resigned after announcing his candidacy for the 2017 presidential elections.
The normalization of the National Front's politics means the party is seen as an inevitable contender.
Sites could be punished with a fine or even with prison sentences.
Hollande's decision leaves an opening for a Socialist to challenge Marine Le Pen and Francois Fillon.
If the former prime minister prevails over Alain Juppe, he will face National Front's Marine Le Pen and a Socialist candidate.
Unpopular president is forecasted to lose a three-way race between Marine Le Pen and the winner of the Les Republicains' primary.
France's presidential frontrunner has been criticised over comments suggesting that Jews had not wanted to integrate in France in the past.
A runoff is expected between Francois Fillon and Alain Juppe for the right to face the National Front's Marine Le Pen in the presidential election in 2017.
Alain Juppe is the favorite, with former president Nicolas Sarkozy and Francois Fillon also vying to face National Front leader Marine Le Pen.
The economic liberal leads favorite Alain Juppé in the center-right primary, according to a survey.