The U.S. will investigate a French plan to impose taxes on technology companies, a move that has been a prelude to new U.S. tariffs under the Trump administration.

U.S. Trade Representative Robert Lighthizer will have as long as a year to examine whether the plan would hurt U.S. technology firms, and suggest remedies. The so-called 301 investigation is the same tool President Donald Trump used to impose tariffs on Chinese goods because of the country’s alleged theft of intellectual property....