Description de torseurs quasi-versels pour une famille de surfaces fibr\'ees en coniques

Generalising work of La Bret`eche, Browning and Peyre and of the author, we describe the geometry required by Manin’s principle and Peyre’s conjecture for a family of conic bundle surfaces containing Ch^atelet surfaces. These surfaces $S_{a,F}$ are the conic bundle surfaces obtained as smooth minimal proper model of $$Y^2-a{Z}^2=F(X,1)$$ with $a\in \mathbf{Z}$ squarefree and $F \in $\mathbf{Z}$[x_1,x_2]$abinaryformof\mathit{\text{even}}degree$n$ without repeated roots and whose irreducible factors over $\mathbf{Q}$ remain irreducible over $\mathbf{Q}\left(\sqrt{a}\right)$.