An installation for fabricating a fiber texture in the form of a strip presenting a profile that varies at least in cross-section includes a loom, one or more take-up rollers, and a storage mandrel, each take-up roller and the storage mandrel presenting a radius that varies across its axial width so as to define an outer surface having a profile in relief. One or more take-up rollers include a plurality of sectors releasably fastened on the outer surface of the take-up roller. Each sector extends over a fraction of the circumference of the take-up roller and over all or part of the axial width of the take-up roller. Each sector also presents at least one thickness that is determined in such a manner as to modify locally the thickness of the profile in relief of the outer surface of the take-up roller.