Ms Le Pen, of the far-right National Front (FN), chose Nicolas Dupont-Aignan, of the mainstream nationalist "Stand Up France" in an apparent bid to attract his voters.
Mr Dupont-Aignan had already backed Ms Le Pen for the second round.
Ms Le Pen faces centrist Emmanuel Macron in the second, decisive round of voting, which takes place on 7 May.
Mr Dupont-Aignan, who got 4.7% in the first round, stood on a platform of leaving the euro and scrapping the European Union, higher ethical standards for elected officials, and focusing on the fight against jihadist terrorism.
He said it was time to stop treating Ms Le Pen as untouchable.
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Emmanuel  Macron
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Marine  Le Pen
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Last updated  April 25, 2017
The polling average line  looks at the five most recent national polls and takes the median value, ie, the value between the two figures that are higher and two figures that are lower.
The BBC's Hugh Schofield, in Paris, says the alliance between the two right-wing parties is symbolically important as it is the first time the FN has formed a pact with a mainstream political party.
Ms Le Pen's manifesto has been adapted to take in some of her putative prime minister's policies.
But the new alliance is less likely to appeal to the nearly 20% of French voters who cast their first round ballot for left-winger Jean-Luc MÃ©lenchon, correspondents say.
Outgoing President FranÃ§ois Hollande, speaking in Brussels at his last EU summit, said the election on 7 May "is a European choice".
"The French have everything to gain by staying in the European Union," he told reporters gathered at the summit to discuss the UK leaving the bloc.
French presidential candidate Marine Le Pen has said she will make a defeated rival her prime minister, if elected.