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Let $X$ be a smooth projective variety over a number field, fibered over acurve, with geometrically integral fibers. We prove that, supposing thefiniteness of $\sha(Jac(C))$, if the fibers over a generalised Hilbertiansubset satisfy the Hasse principle (resp. weak approximation), then theBrauer-Manin obstruction coming from the base curve is the only obstruction tothe Hasse principle (resp. to weak approximation) for zero-cycles of degree 1on $X$.

Principe local-global pour les z\'ero-cycles sur certaines fibrations au-dessus d'une courbe : I