It once looked to many as if President Trump could be a reason for Europe and China to bring their economies closer. His planned tariffs did little to distinguish the European Union, a longtime ally of the United States, from China, the principal challenger to American primacy.

It hasn’t turned out that way.

Instead, the European Union finds itself in a geopolitical chokehold between the world’s two largest economies.

In Brussels, officials are trying to secure a rough trade deal with their American counterparts before Mr. Trump hits the bloc with high, across-the-board tariffs that could clobber the bloc’s economy. At the same time, European Union policymakers are trying to prod their counterparts in Beijing to stop supporting Russia, to stop helping Chinese industry with so much state money and to slow the flow of cheap goods into the European Union.

But at a moment of upheaval in the global trading system, the bloc also needs to keep its relationship with China, the world’s leading manufacturing superpower, on a relatively stable footing.

Leaders from the European Union are scheduled to be in Beijing for a summit in late July, plans for which have been in flux. Hopes for the gathering are low. Even as China pushes the idea that Mr. Trump’s hostility to multilateral trade is prodding Europe into its arms, Europe’s problems with China are only growing.

“There is no China card for Europe,” said Liana Fix, a fellow for Europe at the Council on Foreign Relations.