French President Francois Hollande faced his first political storm on Wednesday as his rightwing opponents looked to exploit an incendiary tweet by his partner just days ahead of a parliamentary election.

The tweet by unofficial first lady Valerie Trierweiler wishing luck to an election opponent of Segolene Royal - Hollande's ex-partner and mother of their four children - was also rounded on by the French press as an 'embarrassment' that threatened to damage the Socialists' electoral chances.

"France's First Gaffe", leftwing daily Liberation wrote on its front page beside a photograph of Trierweiler, saying she had put Hollande 'in a delicate position'.

Rightwing daily Le Figaro went further, saying the Twitter comment had sown "amazement and confusion" among Hollande's Socialist Party and would have 'heavy consequences'.

Royal, who failed in a 2007 presidential bid, is standing against Olivier Falorni, a Socialist dissident, for a parliamentary seat in the western town of La Rochelle.

Hollande has publicly thrown his weight behind Royal, but in the tweet on Tuesday Trierweiler wished Falorni "good luck" and praised his "selfless commitment" to the people of La Rochelle.

The rivalry between the two women has long been a subject of speculation.

Hollande stood loyally by Royal as she battled rightwinger Nicolas Sarkozy for the presidency in the 2007 race, but he had reportedly been in a relationship since 2005 with Trierweiler, a twice-divorced 47-year-old mother of three.

Neither Hollande nor Trierweiler were commenting Wednesday but Prime Minister Jean-Marc Ayrault gave Trierweiler a slight rebuke, saying she needed to learn to be a little more discreet.

"I think she should play a discreet role, which is not easy to figure out," he said. "I understand that things are always a bit complicated at the start, but everyone needs to find their place."

Ayrault accused the right of 'over-exploiting' the incident, as Hollande's opponents jumped on the tweet as an inappropriate intrusion of the president's private life on to the political scene.

The rightwing UMP party of ex-president Sarkozy, whom Hollande defeated in last month's presidential run-off election, is anxious to score points against the Socialists ahead of Sunday's second-round parliamentary vote.

After coming out on top in last Sunday's first round, the Socialists and their allies are expected to win the majority Hollande needs to push through his leftwing programme.

"This affair makes a mockery of our country and of our head of state," Eric Ciotti of the UMP told France Inter radio. "It is a grotesque, ridiculous situation that weakens the position of the head of state."

Some Socialists sought to defuse the crisis by insisting that Trierweiler, a journalist with magazine Paris Match, made the remark in a personal capacity.

But former UMP minister Nathalie Kosciusko-Morizet said Trierweiler's unofficial status was causing "confusion" and that her role should be clarified.

The UMP's Francois Fillon, a former prime minister under Sarkozy, said Hollande should "put his house in order" after the tweet.

"I find this quite sad, but I don't want to comment, I refuse to do what the Socialists did with Nicolas Sarkozy, that is to mix everything together, his private life," he told a radio channel.

An IFOP-Fiducial poll released Wednesday showed Royal losing to Falorni by a vote of 42 to 58 per cent in Sunday's run-off, and Ayrault urged Falorni to 'take his responsibilities' and step aside.

Royal sought to play down the scandal, telling journalists: "Sometimes there can be excitement that we did not want, but it's nothing dramatic.

"That is the reality of political life. What's important is not to lose your way, to stay on a straight line... (and) maintain the dignity of the political debate."

The Socialists and other leftwing parties won about 46 per cent of the vote in Sunday's first round, ahead of the UMP and its allies with 34 per cent.