Anti-terrorist police made the arrests early on Tuesday in the Seine-Maritime department of Normandy and the Cote d’Armor department of Brittany.
Officials in Paris said investigations had brought to light evidence of a link with the Real IRA.
The Real IRA is a breakaway faction of the Irish Republican Army (IRA) which has rejected moves towards a negotiated peace settlement in Northern Ireland.
A small Breton nationalist group – the Breton Revolutionary Army (ARB) – has in the past provided logistical support to the armed Spanish Basque separatist group ETA.
It is believed to have been behind the bombing of a McDonald’s restaurant in Brittany in 2000 that killed a female employee.
The Real IRA split from the IRA – Northern Ireland’s largest Catholic paramilitary movement – in 1997 in protest at IRA involvement in the Northern Ireland peace process.
In August 1998 it bombed the Northern Irish town of Omagh, killing 29 people. The attack was the worst single atrocity in 30 years of violence in the British province.
It is believed to be responsible for several other attacks, including a series of explosions in London in 2001. Its leader, Michael McKevitt, was jailed for 20 years by a special court in Dublin earlier this year.
Northern Ireland’s mainly Catholic republicans want the province reunited with the Republic of Ireland. The province’s mainly Protestant unionists want to remain attached to the United Kingdom.