Fillon's economic programme is "of an unheard-of brutality", FN leader and presidential candidate Marine Le Pen said on a visit to the French Indian Ocean island of Réunion on Monday.
She and other FN leaders have linked his proposals, which include cutting 500,000 public-service jobs, slashing state health insurance and raising VAT, to the "ultraliberal [economic] demands of the European Union".
Le Pen, whose presidential ambitions were boosted by the UK's Brexit vote, has promised to hold a referendum on France's EU membership if she is elected, a proposal that sharply divides her from the mainstream right.
FN vice-president Florian Philippot, the principal architect of a policy designed to appeal to working-class voters that Fillon has dubbed a "cut-and-paste of the far-left's", called the former prime minister the "candidate of rampant globalisation".
In a tweet he accused him of "opening the door to poverty" by "killing" the French social security system.
While Le Pen declared Fillon an "excellent candidate" from her party's point of view, other prominent FN figures were not so sure.
Family, tradition, patriotism
Her niece, Marion Maréchal Le Pen, a leader of the traditionalist wing of the party which is not keen on the Philippot line, called Fillon's candidacy an "added complication for us".
As his campaign gained momentum, Fillon himself told supporters that the "Le Pen firm" was getting nervous because of his espousal of "French values" and patriotism.
Having voted against same-sex marriage, expressed reserves about abortion and declared that France has a problem with Islam, he has attracted the backing of supporters of the 2012 anti-gay marriage demonstrations and far-right websites such as fdesouche.fr.
The high turnout in the two rounds of the mainstream right-wing primary, along with Fillon's decisive victory, indicates that older conservative voters, many of them practising Catholics, were attracted by Fillon's social conservatism and his references to France's "Christian roots".
Right/far-right battle in May
Those are themes dear to the traditionalist wing of the FN, as well as to part of its electorate, especially in the south of France.
With widespread disillusion with President François Hollande's Socialist government, all recent opinion polls have shown that May's second round is likely to be between the mainstream right and the far right.
According to a Harris Interactive poll published Sunday, Fillon would win a decider against Le Pen 67 per cent to 37 percent.
But, as we have learned from recent events including the right-wing primary, the polls can be wrong.
The FN certainly hopes they are and seems to have decided to present itself as the defender of France's welfare state against a Fillon it has branded a pro-European Thatcherite.