In the sunlight of Normandy, before the surviving American veterans who eight decades ago helped turn the tide of the war against Hitler, President Emmanuel Macron of France spoke this past week of the “bond of blood shed for liberty” that ties his country to the United States.

It is a bond that goes all the way back to the founding of the United States in 1776 and the decisive French support for American independence against the British. Tempestuous, often strained as France bristles at American postwar leadership in Europe, the ties between Paris and Washington are nonetheless resilient.

President Biden’s five-day stay in France, an exceptionally long visit for an American president, especially in an election year, is a powerful testament to that friendship. But it illustrates its double-edged nature. French gratitude for American sacrifice as ever vies uneasily with Gaullist restiveness over any hint of subservience.

Those competing strands will form the backdrop of a lavish state dinner at the Élysée Palace on Saturday, when Mr. Macron will reciprocate the state visit that Mr. Biden hosted for him at the White House in December 2022, the first of his administration.

The toasts and bonhomie will not fully mask the tensions between Washington and Paris — over the war in Gaza, how best to support Ukraine and the unpredictable ways Mr. Macron tries to assert France’s independence from the United States.