PARIS — The far-right party of Marine Le Pen was poised to make major gains after the first round of voting in regional French elections on Sunday in the wake of terrorist attacks that traumatized the country last month.

When the votes were counted, Ms. Le Pen’s National Front party was pulling far ahead in two of France’s 13 regions and leading in four others. Trailing were the right-leaning parties, including the Republicains, led by former President Nicolas Sarkozy. Even further behind were the Socialists, whose best-known figure is President François Hollande.

Appearing before her supporters, Ms. Le Pen called it a “magnificent” result, saying the National Front was “the only party that can reconquer the lost territories of the republic, of Calais, where we won 50 percent of the votes, or of the suburbs.” What Ms. Le Pen described as “lost territories” were the French city of Calais on the English Channel, which now has more than 4,000 migrants on its doorstep hoping to reach Britain, and the suburbs of major French cities, many of which have sizable Muslim populations.

The National Front “is the only party to defend an authentically French republic,” she added, and to be dedicated to “the preservation of our way of life.”