PARIS — Nicolas Sarkozy, the flamboyant former French president who had hoped to revive his political career, is facing a formal investigation over allegations that his 2007 campaign received illegal funding from the Libyan strongman Col. Muammar el-Qaddafi.

It is not certain that Mr. Sarkozy, who led France from 2007 to 2012 but failed to generate enough enthusiasm in his 2016 comeback bid, will stand trial. But the decision by investigators to pursue the case represents a significant step and means that a return to the political stage is even more unlikely for Mr. Sarkozy.

Mr. Sarkozy acknowledged as much on Thursday, saying in a television interview, “Politics, that’s over.”

Here are some answers to the central questions about the case.

What happened this week?

After two days of questioning by the police, Mr. Sarkozy, 63, who has been the subject of several corruption inquiries, was formally charged with passive corruption, illegal campaign financing and misappropriation of Libyan public funds. (The charge of passive corruption applies to people suspected of receiving money or favors.)