The French television station BFM said the source said security forces arrested people this morning on suspicion of submitting an "imprecise and easy-going" plan for "violent action" against Emmanuel Macron.
According to the report, these individuals were right-wing extremists, although this has not been independently confirmed.
Security services arrested suspected suspects in Isere, southeast of Lyon; Moselle, on the border with Germany and Luxembourg; and in Ille-et-Vilaine, northwest of Rennes.
It is not known what connection exists between the six arrested persons and how they came into contact with each other.
This is Mr. Macron's second major fear of security in 16 months after a 23-year-old man was arrested and charged with a plot to kill him in a July 2017 Bastille Day parade.
The authorities were alerted to the unnamed man after he talked about buying a gun while playing video games online with other participants.
As officers approached the suspect, they found three knives in his car. He also used the internet to search for potential targets.
According to a report by the French international news agency AFP, he was described as a far-right extremist with hatred for "Muslims, Jews, blacks and homosexuals".
The news of Mr Macron's latest conspiracy comes just hours after his devastating attack on the European Union. He again called for calls to speed up the plans for a "true European army" to ensure that the member states of the bloc are protected from growing military threats.
The French President continued to defend his manifesto for next year's European elections. Brussels needs to step up efforts to build a new Europe-wide army.
He has repeatedly called on the EU to arm itself with a strong and robust defense force so that it can no longer rely on the increasingly volatile US and NATO on security issues.
In a conversation with the Paris radio station Europe 1 Mr. Macron raged: "We need to protect ourselves in relation to China, Russia and even the United States of America.
"If I see, as President Trump announces, that he has abandoned an important disarmament treaty created after the euro-zone crisis of the 1980s in Europe, who is the main victim? Europe and its security.
"We will not protect the Europeans if we do not choose a true European army."
With the exception of France and the UK, NATO members from across Europe have relied heavily on American firepower to protect them since World War II.
Mr. Macron called the increasing Russian hostility in recent months as the main cause of concern and strengthened his calls for a European defense force.
He continued, "Against Russia, which is on our frontier and has shown that it can be a threat, I want to build a real security debate with Russia, a country that I respect, that is European.
"We have to have a Europe that defends itself and depends not only on the United States – and more sovereign."
The French President also suggested that a stronger EU would have a better chance of surviving the increasing threats posed by populist and nationalist movements, whose support has increased in recent years.
He concluded, "I am clear, we live in a Europe that has been broken by the rise of nationalism, we need a stronger Europe so that history will not be repeated."