The invention concerns fluorofunctional statistical polymers of formula (V1), wherein: X, Y and Z represent a hydrogen atom and exhibiting in particular low glass transition temperatures obtained in particular from a monomer of formula (I): F2C=CF-RF-SO2F, wherein: RF represents one or several vinylidene fluoride units and/or a hexafluoropropene unit and/or a chlorotrifluoroerthylene unit. The crosslinkable fluorosulphonated elastomers thus obtained are advantageously usable for making membranes, polymeric electrolytes, ionomers, membranes for fuel cells in particular hydrogen or methanol fuel cells, for obtaining gaskets and O-rings, rubber hose, pipes, pump bodies, diaphragms, piston heads (used in aeronautics, oil, automotive, mining and nuclear industries) and for plastics processes (as processing aids).