A growing anti-trade movement across Europe is posing a serious threat to the future of the Canada-European Union trade deal.

Street protests, petitions and now a lawsuit in Germany against the Comprehensive Economic and Trade Agreement, or CETA, reflect a rising tide of opposition to the agreement that opponents say undermines national sovereignty.

The Canadian deal has become a lightning rod for mounting concerns in many European countries about free trade in general and the ongoing negotiations between the United States and the EU over the Transatlantic Trade and Investment Partnership, or TTIP. That deal is modelled largely on CETA, which has been completed and is awaiting ratification by the European parliament and member states, making CETA a handy target for opponents. Polls in Germany show a large majority of the population is against TTIP and CETA, and opposition has been building in France where many mayors have come out against both deals.

CETA and TTIP are “part of a new generation of trade deals which are much more far reaching than trade deals we’ve had so far,” said Jorg Haas, a spokesman for Campact, a social activist organization in Germany that has nearly two million members and has launched a campaign against CETA. “Past trade deals are essentially about the exchange of goods or about tariffs. But this trade deal infringes upon non-tariff barriers. It goes much deeper. It goes into the whole area of services and services are essentially everything, everything can be considered a service.”

Campact and two other groups filed a lawsuit this week in a German court arguing that CETA violates the country’s constitution because it takes away powers from parliament. For example, the lawsuit argues provisions in CETA would create a council that would act as a kind of lawmaking entity that could change national regulations, something they say only the German parliament has the power to do.

Leading the case is a high-profile German constitutional lawyer, Bernhard Kempen, who is director of the international law institute at Cologne University.

“Ceta is not only dangerous in democratic-political terms but also alarming in constitutional law terms,” Mr. Kempen said in a statement. “The constitutional court’s previous judgments lead only to the conclusion that international legal treaties of this kind do not correspond with the constitution.”

The government of Angela Merkel has expressed support for TTIP and CETA, and has vowed to push for approval of CETA in the German parliament, which is expected to vote on the agreement this fall. But there are signs Ms. Merkel’s main coalition partner, the Social Democrats, are beginning to waver in their support. That party is to hold a convention this spring and activists are planning a campaign to encourage the party to vote against the deal.

CETA must also be approved by both houses of the German parliament, and there are signs the deal will face opposition in the upper house, or Bundesrat, which represents state governments where parties opposed to the agreement are in power. German protest groups have also gathered more than 70,000 names on a petition against the agreement and demonstrations opposing CETA and TTIP have drawn more than 100,000 people in Berlin and elsewhere.

It’s not just in Germany where CETA could face trouble. It’s unclear what would happen to the agreement if Britain votes to leave the EU on June 23. Prime Minister David Cameron, who wants the country to remain in the EU, has been a strong supporter of CETA. If Britain does leave, the EU would likely be distracted for at least two years as it negotiates a new arrangement with the U.K., putting CETA on a back burner. And in France, President François Hollande has come out against TTIP and unregulated free trade.

Prime Minister Justin Trudeau met with Mr. Hollande and Ms. Merkel at the recent G7 meeting in Japan and urged them to keep CETA on track. “When the middle class are anxious about their economic realities in their future, it’s easy to get trapped in demagoguery and protectionism,” Mr. Trudeau told the leaders.