Meanwhile, in Spanish local elections, Podemos, a new anti-austerity party seen as Spain's answer to Syriza, came third with 14.9 percent of the vote. It gained less votes than the ruling People's Party, which came second.
Reacting to the results on Monday, analysts said Syriza's failure to resolve the mounting economic crisis in Greece, and its increasingly sour relations with Europe, might be putting voters off populist parties, despite opposition to economic reforms and austerity measures.
"Voters (in France and Spain have) confirmed that a Greek-style takeover by right- or left-wing populists in these two countries remains an extremely unlikely scenario," Christian Schulz, senior economist at Berenberg Bank, said in a note Monday.
Read MoreBarroso: Greece should blame itself
"The populists gained, but fell far short of winning. So is Europe's populist threat on the verge of being deflated by its most visible success so far, Syriza's victory in Greece in January?"
The Syriza party came to power in January with promises to "tear up" the onerous austerity measures that were a strict condition of its two international financial bailouts, which totalled 240 billion euros ($260.8 billion). Since then, however, it has retreated from those promises, while asking its euro zone neighbors and creditors for a debt haircut, which has been refused.
A number of high-profile spats between German and Greek ministers have cause diplomatic relations to deteriorate further, and Greek Prime Minister is in Berlin Monday for talks with German Chancellor Angela Merkel.
"Local specificities played a major role. But the economic and financial disaster Syriza has triggered in Greece in a record-short time period may have confirmed people's suspicions about the populists," he added, suggesting Podemos' star could be "sinking already."
High levels of voter participation suggested the electorate were becoming wary of the risks that well-organised "extremists" of the left or right could pose to their economic well-being, Schulz added.
"The wave of public discontent Syriza and partners had hoped for does not seem big enough to sweep populists railing against Brussels, Berlin and the inconveniences of a globalised economy to power across Europe."