Using 214fb-1 of data recorded by the BABAR detector at the PEPII electron-positron collider, we study the decay Ds+→K+K-e+νe. Except for a small S-wave contribution, the events with K+K- masses in the range 1.01-1.03GeV/c2 correspond to mesons. For Ds+→ e+νe decays, we measure the relative normalization of the Lorentz invariant form factors at q2=0, rV=V(0)/A1(0)=1.849±0.060±0.095, r2=A2(0)/A1(0)=0.763±0. 071±0.065 and the pole mass of the axial-vector form factors mA=(2.28-0.18+0.23±0.18)GeV/c2. Within the same K+K- mass range, we also measure the relative branching fraction B(Ds+→K+K-e+νe)/B(Ds+→K+K- π+)=0.558±0.007±0.016, from which we obtain the total branching fraction B(Ds+→ e+νe)=(2.61±0.03±0.08±0.15) ×10-2. By comparing this value with the predicted decay rate, we extract A1(0)=0.607±0.011±0.019±0.018. The stated uncertainties are statistical, systematic, and from external inputs. © 2008 The American Physical Society.