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Was the deal that Iran came close to negotiating with six world powers in Geneva over the weekend likely to keep Tehran from developing a nuclear weapon? Not according to French Foreign Minister Laurent Fabius, who said that the proposed agreement—to relax economic sanctions while reining in only parts of Iran’s nuclear program—was a “sucker’s deal.” All indications are that it was Mr. Fabius and the French government whose skepticism blocked the bargain intensely sought by the Obama administration and the mullahs in Tehran.

Over the past two decades, no country has been more consistent than France in recognizing Iran’s unrelenting mendacity about its nuclear ambitions. The White House now will undoubtedly try to pressure French President François Hollande to relent. With talks set to resume on Nov. 20, lawmakers on Capitol Hill who want to encourage Mr. Hollande to stand firm now have an opportunity to do so—and to stymie the administration’s efforts—by enacting more hard-hitting economic sanctions on Iran.

Yet in Geneva, even France seems to have joined its partners—the U.S., Russia, China, the U.K. and Germany—in being ready to grant de facto recognition of the Islamic Republic’s “right” to enrich uranium. Iran has plenty of low-grade uranium because its spinning centrifuges have been implicitly accepted by President Obama and U.S. allies. What seems to have troubled the French about the negotiations—but no one else—was that construction would continue on Iran’s heavy-water reactor, giving Tehran a pathway to a plutonium bomb, and that not a single piece of Iran’s nuclear infrastructure would be dismantled.

The perplexing thing about the Obama administration’s recent diplomacy regarding Iran: Messrs. Obama and Secretary of State John Kerry don’t seem to recognize that they will likely never again have as much economic leverage over Tehran as they do right now.

The impact of Euro-American sanctions on Iran is what helped to jump-start the presidential campaign of Hasan Rouhani, who was elected in June on promises to court the West and rescue the economy. Electoral opinion has, of course, never overridden theocracy in the Islamic Republic. But to whatever extent Supreme Leader Ali Khamenei fears popular unrest provoked by sanctions, that trepidation will lessen once economic pressure is relaxed.

The efficacy of sanctions depends on the threat of escalation, where an ever-expanding web of restrictions scares off foreign businesses. Even when sanctions on Iran were violated, that didn’t really matter, because Washington—Congress, really—created an impression that it intended to encircle Iran with an economic minefield.

The sanctions game with Iran has been as much psychological as legal. When the Obama administration sends a signal that it is willing to reduce economic sanctions for little in return, the general impression abroad—reinforced by French objections to the soft American position in Geneva—is that the White House’s resolve is waning.

The White House similarly forfeited whatever military leverage it had over Iran in September by bungling matters in Syria, where Tehran strongly backs Bashar Assad’s regime. When Assad used chemical weapons on his own people, France was unambiguous about its willingness to strike at Assad militarily; it was the U.K. and then the U.S. that backed down.

So where does that leave us? Reports out of Geneva indicate that the Obama administration was ready to unfreeze Iranian assets and ease sanctions on exports, including gold, petrochemicals and the Iranian auto sector, which would have brought tens of billions of dollars to the regime. The White House seems not to appreciate the ironic effect of its attempted deal-making. Any concession on sanctions that releases hard currency to Tehran provides cash that it could spend on its nuclear program—or to aid the Assad regime or any of Iran’s other unsavory friends.

According to the administration’s narrative, Iran’s nuclear pacification is going to happen through a series of ever-increasing “carrots” (read: bribes) delivered by the U.S. and Europe and sold by the “moderate” Rouhani to the hard-core guardians of the Islamic revolution as a reason to devote their nuclear program to purely peaceful purposes.

Epiphanies do happen. It is possible, though highly unlikely, that Mr. Rouhani—the former right-hand man of Hashemi Rafsanjani, who drove the nuclear program in the 1980s and 1990s—now wants to forsake his nuclear legacy. But why would the prospect of easing sanctions help him persuade the Revolutionary Guards and Supreme Leader Khamenei to abandon the cause? They have already invested their pride, billions of dollars and much of their religious authority on the cherished goal of a nuclear-armed Iran. The Geneva negotiations indicate that Mr. Rouhani’s bosses are willing only to make concessions that are easily revoked or not much of a nuclear impediment to start with.

The U.S. and its allies seem much more likely to get the attention of the supreme leader and the Revolutionary Guards if the pain from sanctions is so intense that a choice has to be made between economic collapse and the nuclear program.

America’s capacity to inflict more pain on those who are driving Tehran’s nuclear effort is substantial. New financial sanctions could lock up all of Iran’s currency reserves—around $70 to $80 billion—held abroad, which would effectively shut down non-humanitarian imports and collapse the rial, Iran’s currency. Financial relief would only come when Iran takes steps to verifiably and irreversibly dismantle its military-nuclear program—and only through controllable accounts, in Europe, where Tehran could exchange funds for industrial goods.

Even new sanctions may not be enough to stop the Islamic Republic’s nuclear ambitions. But after the debacle of American policy in Syria, sanctions are really the only hammer the U.S. has left. America would have a strong hand in negotiations with Iran if President Obama were serious about leaving “all options on the table”—including the threat of military action. His hand might be decent if he were prepared to play economic hardball. But he has to be prepared to fail in order to win. It’s the price of admission to power politics in the Middle East.

Mr. Dubowitz is the executive director of the Foundation for Defense of Democracies and heads its Iran sanctions and nonproliferation projects. Mr. Gerecht, a former Iran-targets officer in the CIA’s clandestine service, is a senior fellow at the foundation.