The three men and a woman, described by security services as radical Islamists, were arrested in Paris and a northern suburb in dawn raids.
A number of French media websites, including Mediapart, were briefly unavailable after a suspected cyber attack hit their web host.
Thomas Dupuy, a sergeant from a commando parachutist unit in the air force, reportedly died in a fierce clash with Islamist militants.
The rally in the hometown of the hostage beheaded by Algerian Islamists, came as flags were lowered to halfmast across France in mourning.
France has authenticated a video of the beheading of Hervé Gourdel, which President Hollande said was a 'cruel and cowardly' act.
An Algerian Islamist group captured the 55 year-old tourist on Sunday and threatened to execute him unless France halted strikes against IS.
Among those dead is Omar Ould Hamaha, known as 'Red Beard', a commander of armed groups who occupied northern Mali in 2012.
In a video released by his captors, Francis Collomp, kidnapped last December, asked for French and Nigerian help in securing his release.
French and Malian troops were engaged this weekend in a battle with Islamist rebels who resurfaced in the northern Mali town of Timbuktu.
Police found weapons and explosives at the home of one of the suspects in the town of Marignane, near Marseille.
French president does not name 'terrorist leaders' killed in recent fighting in Mali, where a fourth member of French forces died on Wednesday.
Islamist chief Abdelhamid Abou Zeid is 'probably' dead, says French military, while the fate of his ally Mokhtar Belmokhtar is more uncertain.
About 1,000 forces from France, Mali and other African countries are now in the town of Bourem, according to a French military official.
France says a sandstorm is preventing its forces from entering the town of Kidal in northern Mali in their offensive against Islamist militants.