The FN currently holds only two council seats out of 101 in the whole country and is likely to win only a handful more in the upcoming elections, said Barroso.
Nonetheless, any gain would build on the FN's recent successes in last year's elections for the EU's parliament, when it gained the largest share of the vote in France, and galvanize the party's leader, Marine Le Pen, toward a presidential bid in the2017 general election.
"The polls certainly point towards a strong showing for the Front National in this weekend's local elections. This would certainly be a political blow for President Hollande and the Socialist Party," Jessica Hinds, European economist at Capital Economics, told CNBC on Wednesday.
The popularity of the FN has grown in France under Le Pen, who succeeded her father, Jean-Marie, in 2011. She has strived to rid party of its racist, anti-Semitic image and to tap into growing disenchantment across Europe with establishment politics and politicians, as well as to benefit from frustration with slow pace of France's economic recovery.
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"The financial crisis has become a political crisis in Europe," Barroso said.
"In France, they (the electorate) are disappointed with the current economic situation and there is massive disaffection towards the establishment—and this, by the way, is something that is going on across Europe, in many countries, like Spain, the U.K. and Greece."