Also missing here is Israel’s active role in fueling opposition to this or, arguably, any agreement with Iran. In the United States, pro-Israel groups have spent heavily on a campaign to block the deal in the Congress, organizing meetings with Israeli diplomats and a videoconference with Prime Minister Benjamin Netanyahu of Israel, who has called the deal a “stunning historic mistake” that threatens Israel’s existence.

Although France’s main Jewish organization has expressed “very serious doubts” about the Iran deal, Mr. Grand said, its objections have not spilled into the political sphere.

“Netanyahu’s opposition was so extreme that it made it difficult for it to exist in any French debate,” he said. “Even critics couldn’t sign up to the Netanyahu narrative because it doesn’t offer a constructive solution.”

And then there is the money — huge sums being spent mainly by the pro-Israel groups, less by supporters of the deal — which shock Europeans unused to this kind of profligate lobbying. Some here are also baffled by the hyperbole coming out of Washington, with talk of a choice between war and peace, and oblique references to the Holocaust.

As seen from this side of the Atlantic, the shrill tone of the debate has worrying consequences, particularly when Republican presidential candidates talk about “undoing” the deal or when Senator Chuck Schumer, Democrat of New York, suggests keeping sanctions in place to prevent American and foreign companies from doing business in Iran.

Europeans regard sanctions as a diplomatic tool, the means to an end. Their concern here is that the Americans will use them as a form of open-ended punishment. “How this debate develops on Iran could potentially be a test case on sanctions,” said Ms. Geranmayeh, of the European Council on Foreign Relations. “The U.S. Congress may underestimate how much their debate is going to have repercussions on sanctions unity.”

Even if the deal survives its congressional roller coaster, the words spoken in the heat of this summer’s debate are a matter of “serious concern,” said Mr. Grand of the Strategic Research Foundation. “It is broader than the Iran issue.” he said. “The problem is that the partisan nature of U.S. foreign policy is making it difficult to manage for its partners. It means you always have doubts that a major foreign policy initiative by a U.S. president will survive.”