Baye had won her first Cesar as Best Supporting Actress for Jean-Luc Godard's "Sauve qui peut .., la vie/Every Man For Himself" (1979), as a woman leaving her husband for a life in the country, and would later reteamed with the director for "Detective" (1984). Her second Best Supporting Actress Cesar was for "Une etrange affaire" (1981), again as an unhappily married woman. In 1990, the actress had one of her best roles as an actress who sacrifices her family in pursuit of fame and fortune in "Every Other Weekend", a role that was written expressly for her. Baye also shone as a pregnant, HIV-positive woman in "Mensonge/The Lie" (1993) and portrayed Dr. Francoise Borre, who worked on the identification of the HIV virus, in HBO's Emmy-winning "And the Band Played On" (1993).
As the 90s drew to a close and she approached an age when most actress find it difficult securing leading roles, Baye continued to offer superlative performances. In 1998's "Venus Beaute Institut", written and directed by Tonie Marshall, she essayed Angele, a fortyish beautician who has shut herself off from the possibility of love only to be ardently pursued by a young sculptor. The following year, Baye turned in a strong, sensual portrayal as a woman who seeks to satisfy a sexual fantasy via a personal ad which leads to an odd and touching relationship in "Une Liaison pornographique/An Affair of Love". She then played a victim of blackmail in the drama "Selon Matthieu/According to Matthieu" (2000).