Solar flare accelerated electron beams propagating through the solar wind plasma are efficient in Langmuir wave generation. The electric field of Langmuir waves associated with solar type III radio bursts is observed in-situ to be clumpy; commonly attributed to the density turbulence of the solar wind. However, exactly how the density fluctuations affect the distribution of the electric field is not known quantitatively. Using weak-turbulence simulations, we self-consistently model the beam propagation and generation of Langmuir waves from the Sun to the Earth. We show how the field distribution changes as an electron beam propagates through the solar corona and the inner heliosphere. We demonstrate that density fluctuations cause the electric field distribution to spread out more uniformly in magnitude as the level of turbulence increases. The results are consistent with the resonance broadening of Langmuir waves. Our simulations provide predictions of the radial behaviour of the Langmuir wave distribution for the upcoming Solar Orbiter and Solar Probe Plus observations in the inner heliosphere.