Using 2.92 fb−1 of electron-positron annihilation data collected at a center-of-mass energy of s√=3.773 GeV with the BESIII detector, we present an improved measurement of the branching fraction B(D+→ωe+νe)=(1.63±0.11±0.08)×10−3. The parameters defining the corresponding hadronic form factor ratios at zero momentum transfer are determined for the first time; we measure them to be rV=1.24±0.09±0.06 and r2=1.06±0.15±0.05. The first and second uncertainties are statistical and systematic, respectively. We also search for the decay D+→ϕe+νe. An improved upper limit B(D+→ϕe+νe)<1.3×10−5 is set at 90% confidence level.