PARIS — President Sarkozy of France and his elegant but enigmatic wife, Cecilia, have divorced after months of questions about their relationship, a first for France that struck a deep, personal blow to his young presidency.

Their lawyer, Michele Cahen, said today that the two were heard Monday by a judge who granted their divorce after nearly 11 years of marriage. She would not say when the divorce proceedings had begun.

In a 15-word statement, Mr. Sarkozy’s office said the two were separating by mutual consent and would not comment further. Mr. Sarkozy’s spokesman said separation meant divorce.

The announcement raised questions about how the couple could secure a divorce so quickly, which no one in the president’s office would answer.

Although previous leaders in France have had extramarital affairs, the Sarkozys are the first French presidential couple to divorce while in power.

Their split came as Mr. Sarkozy faced his first major political challenge: nationwide transportation strikes that caused bus, train, and subway service to ground to a halt across France.

Mr. Sarkozy has not given any hint that his marital troubles will dent his determination to push ahead with his ambitious program of economic, political, and social reforms for France. In the past week, as speculation about his marriage reached new heights, he continued to present an image of business as normal. He was to be in Portugal today for a European Union summit.

Nicolas and Cecilia Sarkozy split for a few months in 2005, and she had seemed ill at ease as first lady since her husband’s election in May. She did not cast a ballot in the runoff, and has rarely appeared with her husband in public recently.

Her one political venture came back to sting her: She raised her profile dramatically during a July mission to seek the release of five Bulgarian medical workers and a Palestinian Arab doctor jailed in Libya. The stunned French media questioned her diplomatic credentials, and parliament is investigating arms deals signed soon after the release.

“She was shaken, murdered, wounded by the controversy,” a friend of the couple, Isabelle Balkany, told France Inter radio.

“Cecilia is a woman of conviction who needs to do things, feel useful. She knew that she would have trouble tolerating the conventional side” of being a president’s wife, she said.

Ms. Balkany predicted the split would not affect the president’s job.

Even if he is “affected to his depths” by the “painful” decision, she said, “I sincerely think that it will have absolutely no impact on his mission as chief of state.”

Cecilia Sarkozy accompanied Mr. Sarkozy through the recent years of his political career, acting as an aide, confidante, and an ever-present figure at political events.

Dynamic and ambitious, they tried to buck conventions in French politics, she in designer denim and he jogging and speaking in straight, inelegant sound bites.

Their planned divorce also broke precedent and puts Nicolas Sarkozy apart from France’s past leaders.

In 2005, photos of Cecilia hand-in-hand with another man on a Manhattan sidewalk were splashed across a magazine cover.

Mr. Sarkozy talked about it on national television, saying: “Like millions of families, mine has experienced some difficulties.”

Observers wondered then whether Mr. Sarkozy could become president without her support and presence beside him. The question turned out to be moot, as she came back in time for his presidential push.

News reports yesterday said the couple had seen a judge to say they are seeking a formal separation, prompting debate among experts over whether the constitution allows them to divorce because of the strong legal protections designed to keep sitting presidents out of court.

Both Sarkozys have been previously married. They have two children each from their previous marriages, as well as their own son, Louis.

Until the Sarkozys, French presidents’ private lives remained largely private. But Mr. Sarkozy courted the spotlight for years in his long run-up to the presidency — and that has meant his marital troubles were front-page news.

“The couple was quite extraordinary, really fused together,” a political journalist and author of “Tigers and Tigresses,” a book about presidential couples in modern France, Christine Clerc, said.

“They became an ordinary couple, a couple like many others who don’t get on well anymore after 14 years, but who have a child in common, who had many projects in common, who have a deep bond, and who have lived many things together,” she said.

The timing of the announcement could help Mr. Sarkozy on another front, by knocking the nationwide strikes off front pages.

The daily Liberation devoted five pages and its front page to Mr. Sarkozy’s marriage today, relegating the strikes to inside pages — even though the newspaper traditionally leans left and might have been expected to devote more attention to the labor unrest had the presidential couple not overshadowed it.

Protesters at a union-led march in Paris today had little sympathy for Mr. Sarkozy’s personal woes.

“There are problems more serious than that,” a 63-year-old marching to protect retirement benefits, Yvelle Franck, said.