Agents from the French domestic security agency, backed by elite police units, conducted the arrests.
The two men "intended to commit an attack on French soil in the very short term, which is to say in coming days", Interior Minister Matthias Fekl said at a brief news conference.
French Interior Minister Matthias Fekl speaks to reporters.
Separately, sources in the camp of conservative Francois Fillon said they had been warned there was a security risk for the right-wing candidate. The men had been "radicalized" and were known to the French intelligence services, he added.
Reports claim a video made by the two men in which they declared allegiance to ISIS was found and that a newspaper front page showing the candidate they meant to target was also found in their possession.
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France has remained on high alert since a string of terror attacks that began in 2015, which have killed over 230 people.
Candidates have been heavily guarded during the election campaign, and until now there had been few security scares.
Officers have been hunting the pair since last week and arrested them within minutes of each other on Tuesday.
Mr Fekl said police were carrying out searches and that security surrounding the elections and the candidates had been strengthened.
The anti-EU, anti-immigration Front National leader is polling just behind Emmanuel Macron, the Europhile centrist given the best chance of beating her in a runoff.
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