In a statement on Tuesday, the press offfice for the Grand Mufti said it "had informed the presidential candidate, through one of her assistants, of the need to cover her head when she meets his eminence, according to the protocol assumed by Dar al-Fatwa", the highest Sunni authority in Lebanon.
Her chief of staff was placed under formal investigation over the alleged misuse of European Union funds to pay parliamentary assistants, French media report.
The party added: "This is obviously a media operation whose sole goal is to attempt to disrupt the smooth running of the presidential election campaign and to try to harm Marine Le Pen at the very moment when her candidacy has made a major breakthrough in voting intentions, especially for the second round".
Ms Le Pen said: "I clearly explained that in the political picture the least bad option is the politically realistic".
Syria dominated Lebanese government and politics for years and had a military presence in the country until 2005, when it withdrew following the assassination of Saad's father, former Prime Minister Rafik al-Hariri, and months of anti-Syria protests.
Asked whether it was the first time a British Prime Minister had met a French presidential candidate, the spokesman said Tony Blair had met Nicolas Sarkozy in 2007. Critics say that her anti-immigrant, anti-EU stance is cover for an islamophobic and xenophobic agenda. She said Syrian President Bashar Assad was "the most reassuring solution for France", adding that the best way to protect minority Christians is to "eradicate" the Islamic State group preying on them - not turn them into refugees.
Le Pen has proposed leaving the euro zone, taxing imports and on-the-job contracts of foreigners, lowering the retirement age and making foreigners pay for their children to go to schools free to French citizens.
In the second round, Mr Macron would beat Ms Le Pen by 61% to 39%, while Mr Fillon would also defeat the far-right candidate, but by 57% to 43%.
The declaration pushed the euro up against the dollar, and French bond yields, which had risen because of fears of rising support for Le Pen, fell about 5 basis points.
Le Pen was also clearly using her two-day visit to the former French protectorate - and her unusual encounter with a foreign president - to appeal to the thousands of French voters in Lebanon.
In some polls Mr Macron is second after Marine Le Pen for the first round of the French Presidential elections.
Three recent opinion polls indicate that Fillon has either edged back to being even with Macron or has taken a small lead.