France’s Socialists are hoping that François Hollande’s popularity surge as a result of his handling of the Paris terrorist attacks is about to bring the party’s long losing streak to an end.

A byelection in eastern France is set to return a Socialist party (PS) candidate, despite a close-run second-round runoff with the far-right Front National (FN), which led the first vote a week ago.

The vote has sparked controversy: the opposition centre-right UMP party – backed by its leader, former president Nicolas Sarkozy – has decided not to advise supporters to vote PS to block the FN. A number of leading UMP heavyweights, including former prime minister Alain Juppé, a Sarkozy rival, have openly defied the party’s decision.

Victory in the Doubs département, on the French-Swiss border, would be the first parliamentary gain for the Socialist government since it came to power in 2012, winning 295 of the 577 seats. Since then it has seen its absolute majority whittled away and was hit with catastrophic showings in local and European elections last year.

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Sunday’s byelection was sparked by former minister Pierre Moscovici’s resignation to take up a post in the European commission. Unless the PS can hold on to the seat, it will lose its absolute majority.

Hollande’s popularity more than doubled in the wake of the attacks on Paris by jihadi gunmen that left 17 people dead. Pollsters Ifop described the jump as “rare and historic”. An Ifop poll last Thursday suggested that the Socialist candidate in Doubs, Frédéric Barbier, would win with 53% against 47%. However, Ifop admitted the vote was so close that it could give no accurate prediction of the results.

The “neither PS nor FN” line taken by the UMP may be decisive. Its candidate, Charles Demouge, was eliminated in the first round of voting and told supporters to vote for his PS rival. However, the UMP has called on them to abstain or cast a blank vote.

Juppé, who is expected to challenge Sarkozy for the party’s presidential nomination in 2017, pointed out that the FN candidate, Sophie Montel, once said that the “inequality of races” was “obvious”. An FN win would give the far right a third seat in the National Assembly and be an indicator for departmental elections in March.

Barbier has admitted that the “margin of error” means there is everything at stake for his party. Montel, 45, has spoken of the “Islamist peril” since the Paris terror attacks.

Government heavyweights Bernard Cazeneuve, the interior minister, and Manuel Valls, the prime minister, visited the Doubs in the runup to the vote. Valls said UMP supporters should remember the “values of the republic and of General de Gaulle” and that it was unthinkable the seat should be held by “someone who believes in racial theories”.

Edwy Plenel, head of the investigative website Mediapart, said there was no “FN wave” and that the result came down to the abstention rate. Only 40% of local voters turned out for the first round. “There’s no [pro-FN] movement in the Doubs, because there is no vote,” he told Sud Est radio.

Former UMP government minister Roselyne Bachelot said the “neither-nor” line was the “worst solution”, telling journalists: “For those who defend this strategy, it means there’s no difference between the Front National and the Parti Socialiste. For me, it’s totally indefensible.”

At a press conference on Wednesday, Hollande reminded voters that in 2002 – when the PS candidate, Lionel Jospin, was knocked out in the first round of the presidential poll, leaving the FN’s Jean-Marie Le Pen in a second round runoff against the UMP’s Jacques Chirac – his party “did not hesitate a second” in advising its voters to support Chirac.

In a clear dig at Sarkozy, Hollande told journalists: “I’m the head of state, not the head of a party, but everyone knows how I feel and everyone knows how I acted in the past when I was head of a party. I don’t say it was easy, but some things have to be done.

“In the republic there are [political] parties who have the right to have candidates and elected representatives. Having said that, are all parties in line with the values of the republic? No, surely not.”