It's worrying that the FN won against a centre-right candidate in the run-off

[muriel_volestrangler]

That may indicate that what voters there were on the left thought "there's no difference - I don't care what my party says about voting for the moderate UMP, I won't vote at all", but even if that is the main cause of this, such apathy concerns me.

There was a left wing candidate in the 1st round - they only got 15%:

The far-right achieved a massive 49.5 percent landslide in the first round of a by-election Sunday in the Brignoles constituency of the Var region of southern France.

National Front (FN) candidate Laurent Lopez took 40.4 percent of the vote, with another far-right party, the “Parti de France”, taking 9.1 percent. The centre-right UMP, France’s main opposition parliamentary party, came second with 20.8 percent.
...
The ruling Socialist Party (PS) was not represented in the by-election, lending its support instead to the Communist candidate Laurent Carratala (14.6 percent).

The PS called for “an assault on the FN” in the second round in favour of the UMP candidate on October 13.

http://www.france24.com/en/20131007-national-front-brignoles-by-election-france-socialist-party-ump