Jordan Bardella, the far-right National Rally leader who may become France’s next prime minister, has repeated the same basic promises since a snap election was called in France.

If his party forms the country’s government, he will greatly reduce immigration, cut taxes and crack down on crime, he says.

But the National Rally is the heir to a political tradition in France associated with overt racism, antisemitism and Holocaust denial, and though the party has distanced itself from that past, some basic philosophies remain embedded in its policies: Immigrants pose a threat to France’s security, economy and national identity.

Among Mr. Bardella’s plans are stripping away the automatic right to French citizenship at age 18 to children born in France to non-French parents; ending free medical treatment for undocumented people, except in emergencies; and restricting citizens with second passports from taking jobs deemed sensitive, like running a nuclear plant and working in “strategic” defense.

He also wants to block convicted criminals from living in public housing and slash the country’s sales tax on all forms of energy, from fuel to electricity.

How he will do these things is not entirely clear. The party’s 21-page program, bursting with photos and graphics, is thick with sweeping ideas but thin on details on how to implement them. And over the past weeks of furious campaigning and debates, Mr. Bardella has backpedaled some pledges or placed them on the shelf for later.