A fibrous preform (1) is produced, provided with a sandwich structure comprising an intermediate flexible core (4) and two outer fibrous frames (2, 3), respectively arranged on opposing outer faces of said flexible core (4) and assembled by sections of wire (8, 9) passing through said fibrous frames (2, 3), said preform (1) being impregnated with resin. Said preform is then hardened and the core (4) is removed, preferably by pre-densification with chemical vapour infiltration, and the structure produced is then densified with liquid-phase infiltration.