The result is a clear setback for Ms Le Pen's National Rally, though it came in second place in most regions, according to early official results and polling agency projections.
The previous record abstentions in a first round of regional elections was in 2010 (53.7 percent), with the highest across all elections set in the 2009 European elections (59.37 percent).
The vote on Sunday was widely watched as the last national electoral test ahead of presidential and parliamentary elections next year which polls now show as being a close race between Le Pen and Macron.
France's far right performed worse than predicted in Sunday's regional elections, exit polls showed, leaving victory in the southern battleground of Provence-Alpes-Cote d'Azur and a platform for the 2022 presidential election in the balance.
"I call on them to respond urgently".
The regional elections are being closely watched for voter preferences ahead of next year's Presidential election.
Sunday's polls were for seats in mainland France's 13 regions and 96 departments. It is hoping to win control of a region for the first time to boost her decade-long effort to legitimize a party long seen as an anti-democratic, anti-Semitic pariah. Exit polls showed her popular lieutenant Thierry Mariani tying with the conservative incumbent Renaud Muselier in Provence-Alpes-Cote-d'Azur, the area around Marseille, the country's second-most populous city, and the French Riviera, where surveys had showed her party winning.
It is hard to predict the ultimate winners of the polls because of the two-round electoral system and the impact of tactical voting, which usually sees mainstream parties gang up to keep the far-right out of power.
However, at a national level, the projected vote share for the RN of around 19 percent is nine points lower than in the last regional polls in 2015.
But the outcome will inevitably shape the narrative in the coming weeks, particularly with regard to the strength and electability of Le Pen, as well as the state of Macron's enfeebled party, the Republic on the Move (LREM).
"Of course we're asking ourselves questions", RN vice-president Jordan Bardella told RMC radio on Monday morning.
Opinion surveys project Le Pen will poll highest in the first round of next year's presidential vote, propelled by a support base fed up with crime, threats to jobs from globalisation and a ruling elite viewed as out of touch with ordinary citizens.
"No-one can be happy when there is a 70 per cent abstention rate, rising to over 80 per cent among young people", he added.
An unprecedentedly high rate - 68% - of the population didn't vote.
"We could say it is a collapse in electoral turnout", political scientist Bruno Cautres from the Cevipof institute at Sciences Po university said.
Several French political personalities looked set to emerge strengthened from Sunday's vote, however, including centre-right presidential hopeful Xavier Bertrand, head of the Upper France region.