But prevailed, as the final result will depend on how parties decide to join forces in each of the country's 577 constituencies for the second round, with horse-trading already under way ahead of next Sunday's runoff.
One poll showed the RN potentially winning an absolute majority.
The euro, which has weakened 0.8% since President Emmanuel Macron called the election on June 9, rose to a more-than-two-week top of $1.076175, according to LSEG data. It was last up 0.4% at $1.075425.
"I think it's a slight 'well, there were no surprises', so there was a sense of relief there," said Fiona Cincotta, senior markets analyst at .
"Le Pen had a slightly smaller margin than some of the polls had pointed to, which may have helped the euro a little bit higher on the open."
The shock vote has rattled markets, as the far-right, as well as the leftwing alliance that came second on Sunday, have pledged big spending increases. Investors have been alarmed, given France's already high budget deficit that has prompted the EU to recommend disciplinary steps.
Last week, the premium that bondholders demand to hold France's debt over Germany's surged to its highest since 2012, during the euro zone debt crisis.
Shares in three heavyweight lenders - Societe Generale , BNP Paribas and Credit Agricole - have dropped between 9% and 14%, leading losses of nearly 7% in the Paris CAC 40 index.
Analysts expect little meaningful recovery in France's bonds.
European stocks were set for a much higher open, with Eurostoxx 50 futures jumping 1.18%, while French OAT bond futures rose 0.22% during Asian hours.
"We struggle to see a material and sustainable snap back," said Peter Goves, head of developed debt sovereign research at MFS Investment Management.
Markets had calmed after the initial turmoil that followed the election announcement, as the RN party toned down some of its more radical plans and said it would respect EU's fiscal rules that require France to cut its deficit, but they took another hit on Friday.
"Markets are especially worried about the fiscal implications of a potential far-right victory on France's budget deficit and debt dynamics," said Vasu Menon, managing director of investment strategy at OCBC in Singapore.
NO RESPITE
Markets were expected to stay volatile, given the high uncertainty over next week's final results.
Much depends on political dealmaking. Candidates through to the run-off have until Tuesday evening to decide whether to stand down or run.
The leftwing alliance would withdraw candidates who finish third on Sunday from the runoff, said Jean-Luc Melenchon, leader of the France Unbowed party.
French bonds could recover if alliances to block the RN from taking power start to look credible, said Kathleen Brooks research director at trading platform XTB.
Fuelling uncertainty, Sunday's high turnout suggests France is heading for a record number of three-way run offs - expected to benefit the RN much more than two-way contests.
"Markets are looking into another week of really high uncertainty. Probably fear, as it is still possible for RN to gain an absolute majority next week," said Carsten Brzeski, global head of macro at ING.
Source: Forex-Markets-Economic Times