WASHINGTON — The arrests came quickly after the Sept. 11, 2001, attacks. There was the Muslim man suspected of making anti-American statements. The Middle Eastern grocer, whose shop, a tipster said, had more clerks than it needed. Soon hundreds of men, mostly Muslims, were in American jails on immigration charges, suspected of being involved in the attacks.

They were not.

After shootings last week at a satirical newspaper and a kosher market in Paris, France finds itself grappling anew with a question the United States is still confronting: how to fight terrorism while protecting civil liberties. The answer is acute in a country that is sharply critical of American counterterrorism policies, which many see as a fearful overreaction to 9/11. Already in Europe, counterterrorism officials have arrested dozens of people, and France is mulling tough new antiterrorism laws.

Many European countries, and France in particular, already have robust counterterrorism laws, some of which American authorities have studied as possible models. But the terrorist rampage at the Charlie Hebdo newspaper offices and the Hyper Cacher market prompted calls to go even further. Valérie Pécresse, a minister under former President Nicolas Sarkozy, said France needed its own version of the USA Patriot Act, which gave the United States more authority to collect intelligence and pointed America’s surveillance apparatus at its citizens.

Politicians and civil rights advocates on both sides of the Atlantic bristled at that suggestion, and at a string of arrests in which French officials used a new antiterrorism law to crack down on what previously would have been considered free speech. One man was sentenced to six months in prison for shouting support for the Charlie Hebdo attackers. Up to 100 others are under investigation for remarks that support or tried to justify terrorism, authorities said.