Bayrou said at a press conference that the country was at "extreme risk" and needed what he described as an "exceptional response."
The Grand Mufti's office expressed surprise at Le Pen's public reaction to headscarf, claiming she had not expressed concern when informed of the plans prior to the engagement.
Sarkozy could face a one-year prison sentence if convicted.
National Front leader vows to expel illegal migrants, curb immigration, take France out of the euro zone and levy protective tariffs.
A survey found 69 percent of people wanted Fillon to drop his bid.
The Front National leader failed to repay €300,000 demanded by the EU Parliament.
Polls failed to predict Brexit or Donald Trump, but online comments are full of the emotions that matter.
While she said she "stands up for free markets," May warned of ordinary voters feeling left behind.
Opinion polls now put Macron in third place, behind Marine le Pen and Francois Fillon.
Far-right populism is on the rise, often in places where economic security and labor rights have diminished.
Le Pen, whose National Front party holds anti-immigrant and anti-European Union views, was seen entering an elevator at the building, according to a Reuters witness, but she did not speak to reporters gathered there.
It won't be plain sailing for the independent candidate, but the latest polls show Emmanuel Macron is the one to watch.
The National Front leader said she did not view the annexation of Crimea as illegal.
Leading contender Manuel Valls, the former prime minister, is seen as not likely to prevent a runoff between conservative Francois Fillon and far-right Marine Le Pen.
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.
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.