Rousseff said she was being pressured to resign because her rivals wanted "to avoid the difficulty of removing - unduly, illegally and criminally - a legitimately elected president from power".
The leftist leader earlier this week ruled out stepping down despite corruption allegations that have prompted impeachment proceedings in parliament and mass protests calling for her ouster.
In the interview, also with Le Monde, New York Times, El Pais and Argentina's Pagina 12, Rousseff said any attempt to remove her from power without legal justification would represent a "coup".
She said any such move would "leave a deep scar on Brazilians' political life".
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But Rousseff, an ex-guerrilla tortured under Brazil's military dictatorship, said she was in favour of protests because she was from "a generation in which if you opened your mouth you could go to jail".
Facing the impeachment proceedings, protests and a splintering coalition, Rousseff called former president Luiz Inacio Lula da Silva to the rescue last week, naming him her chief of staff.
"Violating privacy breaks democracy because it breaks the right of every citizen to a private life," she said, banging the table as she made her point, the Guardian reported.
Lula is now in limbo after a Supreme Court judge blocked his appointment. He needs the full court to reverse that decision, allowing him to take up his job - and the ministerial immunity that comes with it.