Process for manufacturing a CFET device, characterized in that it comprises: - forming a double semiconductor-on-insulator substrate comprising in succession, from its base to its surface: a support substrate, a first electrically insulating layer, a first monocrystalline semiconductor layer, a second electrically insulating layer having a thickness of between 10 and 30 nm, and a second monocrystalline semiconductor layer; - forming trenches from the surface of said substrate to the first electrically insulating layer to form at least one fin, - in each fin, forming a channel for a first transistor in the first semiconductor layer and a channel for a second transistor of the opposite type to the first transistor in the second semiconductor layer, wherein forming the double semiconductor-on-insulator substrate comprises: - a first layer transfer step comprising implanting atomic species into a first donor substrate to form an embrittlement zone therein, bonding said first donor substrate to the support substrate, with the first electrically insulating layer at the bonding interface between the first donor substrate and the support substrate, and detaching the first donor substrate along the embrittlement zone to transfer the first electrically insulating layer and the first monocrystalline semiconductor layer onto the support substrate, thereby forming a first semiconductor-on-insulator substrate, said first layer transfer step further comprising a heat treatment at a sufficiently high temperature to smooth the first monocrystalline semiconductor layer transferred onto the support substrate down to a roughness of less than 0.1 nm RMS, - after said heat treatment, a second layer transfer step comprising implanting atomic species into a second donor substrate to form an embrittlement zone therein, bonding said second donor substrate to the first monocrystalline semiconductor layer of the first semiconductor-on-insulator substrate, the second electrically insulating layer being at the bonding interface between the second donor substrate and the first monocrystalline semiconductor layer, and detaching the second donor substrate along the embrittlement zone to transfer the second electrically insulating layer and the second monocrystalline semiconductor layer onto the first monocrystalline semiconductor layer of the first semiconductor-on-insulator substrate. - forming a double semiconductor-on-insulator substrate comprising in succession, from its base to its surface: a support substrate, a first electrically insulating layer, a first monocrystalline semiconductor layer, a second electrically insulating layer having a thickness of between 10 and 30 nm, and a second monocrystalline semiconductor layer; - forming trenches from the surface of said substrate to the first electrically insulating layer to form at least one fin, - in each fin, forming a channel for a first transistor in the first semiconductor layer and a channel for a second transistor of the opposite type to the first transistor in the second semiconductor layer, - a first layer transfer step comprising implanting atomic species into a first donor substrate to form an embrittlement zone therein, bonding said first donor substrate to the support substrate, with the first electrically insulating layer at the bonding interface between the first donor substrate and the support substrate, and detaching the first donor substrate along the embrittlement zone to transfer the first electrically insulating layer and the first monocrystalline semiconductor layer onto the support substrate, thereby forming a first semiconductor-on-insulator substrate, said first layer transfer step further comprising a heat treatment at a sufficiently high temperature to smooth the first monocrystalline semiconductor layer transferred onto the support substrate down to a roughness of less than 0.1 nm RMS, - after said heat treatment, a second layer transfer step comprising implanting atomic species into a second donor substrate to form an embrittlement zone therein, bonding said second donor substrate to the first monocrystalline semiconductor layer of the first semiconductor-on-insulator substrate, the second electrically insulating layer being at the bonding interface between the second donor substrate and the first monocrystalline semiconductor layer, and detaching the second donor substrate along the embrittlement zone to transfer the second electrically insulating layer and the second monocrystalline semiconductor layer onto the first monocrystalline semiconductor layer of the first semiconductor-on-insulator substrate.