Socialist candidates failed to win the most votes in all three of the first-round by-elections held on Sunday, six months after the left swept to power.
Candidates backed by the right-wing main opposition UMP took first place in the by-elections for seats in Val-de-Marne, Herault and Hauts-de-Seine, despite damage to the party's reputation from an ongoing leadership crisis.
In the Val-de-Marne constituency in suburban Paris, the Socialist candidate was eliminated altogether while in the other two votes right-wing candidates were far ahead.
Run-off votes will be held on Sunday.
After sweeping to power thanks to discontent with right-winger Nicolas Sarkozy, Hollande has seen his popularity plummet in recent months as France's economy stagnates and unemployment rises.
The UMP hailed the results as a "warning" to the government but the Socialists noted that the three seats are traditionally held by the right.