In 2012 Front National (FP) member Marion Maréchal-Le Pen was elected the youngest member of the French Assembly in modern political history. Marion is nationalistic. She opposed Gay Marriage in France and pushes for immigration restrictions.
Liberals often accuse conservatives of being "old white men;" but while they might be white, the New Right is not old.

In Scotland, the independence movement is being backed by the youngest generation of voters.

Yahoo News:
"The campaign for Scottish independence took to the family dinner table this weekend as young nationalist voters were urged to use Sunday lunch to persuade their grandparents to vote 'Yes' in next week's referendum.
People over the age of 65 are the group most resistant to the overtures of Scottish National Party (SNP) leader Alex Salmond and his team, opinion polls suggest.
But many young people, often 16 and 17-year-olds who will vote for the first time on Thursday, are expected to back change - and are being urged to use all their charms with elderly relatives as the campaign goes down to the wire."
The Scottish National Party is only a part of the burgeoning New Right movement in Europe which strongly trends towards populism, anti-immigration, anti-EU, and anti-multiculturalist sentiment. They oppose the cultural Marxist agenda to reshape Europe into a globalized polyglot of races, religions, and cultures.

Another component of the New Right is the now largest party in France, the Front National led by Marine Le Pen, the daughter of its traditionalist founder.

As BBC News reported:
"Commentators have been struck by other changes in the FN [Front National] vote this time. There are more young people. According to pre-vote polls, 25 % of 18-24 year-olds were planning to vote for Marine Le Pen. The given explanation is that young people are increasingly pessimistic, and see little hope in the mainstream political argument."
In that same election (2012), 18% of the country was voting for Marine Le Pen, so her 25% among the 18-24 year old demographic represents a youthful platform.

Why are young people the driving force behind New Right nationalist movements in Europe?

Most likely because they've sensed multiculturalism represents their own disenfranchisement, the destruction of every component of their identities, and more mass-immigration of low IQ minority races that will rob them of jobs.