Rachida Dati announced her pregnancy in the fall. She is single and says it's none of anyone's business who the father is.
Conventional wisdom has it that the French media and public are much more gracious than the American media and public about leaving their politicians' private lives out of the public sphere. And perhaps this is true. Exhibit number one is usually Mitterand's illegitimate daughter Mazarine Pingeot, whose relationship to Mitterand was not revealed by the press
Nonetheless, look at the most popular searches that came up as I typed Dati's name into teh Google:

Enceinte is 'pregnant', pere is of course père, 'father', enceinte de qui 'pregnant by whom'.
Then we get ivre 'drunk', nue 'naked', then Bernard Laporte, who was rumored to be the father but denied it, and Paris Match, which is a celebrity magazine that Dati has appeared in, to much criticism.
In any case... evidently someone cares about Dati's extracurricular activities.