The winner was the incumbent MP, Jean-François Mancel of the right-wing UMP, who won 40.61 per cent of the vote.
With a score of 21.37 of the vote, Socialist Sylvie Houssin is now eliminated and there will be a second round runoff between the Front National’s Florence Italiani and the UMP candidate.
Socialist Party leader Harlem Désir has called upon Socialist voters to vote for the UMP candidate in order to stop a possible Front National victory.
Although the Socialists did not expect to win the by-election, they are taking stock of a result which signals considerable dissatisfaction amongst their own supporters.
In the last election in the constituency, in the June 2012 parliamentary elections, the Socialist result was only 63 votes behind the UMP’s winning score, although that result was then invalidated after a challenge from Houssin.
This weekend's turnout was low, with just over two thirds of voters choosing to abstain.
The failure of the Socialist candidate to make the second round will do nothing to raise the morale President François Hollande and Prime Minister Jean-Marc Ayrault, who are both plummeting in opinion polls.
The latest figures released today (Opinion Way survey) show that 67 per cent of those polled are unhappy with Hollande’s actions, 10 per cent higher than the February figure. Among left-wing voters there has been a 13 per cent increase in dissatisfaction compared to last month.
Hollande visited both Dijon and Bordeaux last week in a bid to get around the country and meet more people, though on his visit to Dijon, he faced some angry locals in one of the poorer districts.
Next week Hollande will appear on French television to outline some of the country’s difficulties and how he hopes to deal with them.
Prime Minister Jean-Marc Ayrault is also trailing in opinion polls, with only 31 per cent of those polled expressing satisfaction.
Ayrault also faces a vote of confidence on Wednesday but as the Socialists have a comfortable majority in the French lower house of parliament, he will win the vote easily.
Ayrault’s supporters insist the vote has more to do with the internal party politics of the right- wing opposition UMP and its contested boss Jean-François Copé, who is keen to bolster his credibility after November’s bitter party leadership battle.
Copé is behind the no confidence motion.