  Tailoring the properties of correlated oxides is accomplished by chemical
doping, pressure, temperature or magnetic field. Photoexcitation is a valid
alternative to reach out-of-equilibrium states otherwise inaccessible. Here, we
quantitatively estimate the coupling between a lattice distortion and the
charge-transfer excitation in (La$_2$CuO$_{4+\delta}$). We photoinduce a
coherent La ion vibration and monitor the response of the optical constants in
a broad energy range, providing quantitative information on the electron-phonon
matrix element that can be compared to theoretical models. We propose the same
methodology to probe electron-electron interactions in other materials.
