The nonlinear response of single GaAs quantum dots is studied in femtosecond near-field pump-probe experiments. At negative time delays, transient reflectivity spectra show pronounced oscillatory structure around the quantum dot exciton line, providing the first evidence for a perturbed free induction decay of the excitonic polarization. Phase-disturbing Coulomb interactions between the excitonic polarization and continuum excitations dominate the optical nonlinearity on ultrafast time scales. A theoretical analysis based on the semiconductor Bloch equations accounts for this behavior.