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The spin dynamics of the geometrically frustrated triangular antiferromagnet multiferroic CuCrO2 have been mapped out using inelastic neutron scattering. The relevant spin Hamiltonian parameters modelling the incommensurate modulated helicoid have been determined, and correspond to antiferromagnetic nearest and next-nearest neighbour interactions in the ab plane, with a strong planar anisotropy. The weakly dispersive excitation along c reflects the essentially two-dimensional character of the magnetic interactions and according to classical energy calculations it is weakly ferromagnetic. Our results clearly point out the relevance of the balance between a ferromagnetic coupling between adjacent planes and a weakly antiferromagnetic next-nearest neighbour interaction in stabilising the three-dimensional ferroelectric magnetic order in CuCrO2. This novel insight on the interplay between magnetic interactions in CuCrO2 should provide a useful basis in the design of new delafossite-based multiferroic materials.