The authorities say that the detainees had an imprecise and ill-defined plan to attack the French president.
The source said that the French security services had arrested the six suspects to prepare an “imprecise and ill-defined” plan to carry out a “violent action” against the president.
The French television channel BFM TV said that the six detainees were members of the extreme right, but that could not be confirmed independently.
The arrests were made in three areas of France. Isere, in the southeast of Lyon; in Moselle, on the border with Germany and Luxembourg; and in Ille-et-Vilaine, in the northwest near the city of Rennes.
It was not immediately clear what was the link between the arrested or how they were in contact.
In an interview published on Sunday, Macron warned of the threat of far-right movements in Europe and claimed that complacency in the 1930s was what opened the way for the rise of Hitler in Germany and Mussolini in Italy.