The problem of beam alignment (BA) in a cell-free massive multiple-input multiple-output (CF-mMIMO) system operating at millimeter wave (mmWaves) carrier frequencies is considered in this paper. Two estimation algorithms are proposed, in association with a protocol that permits simultaneous estimation, on a shared set of frequencies, for each user equipment (UE), of the direction of arrival and departure of the radio waves associated to the strongest propagation paths from each of the surrounding access points (APs), so that UE-AP association can take place. The proposed procedure relies on the existence of a reliable control channel at sub-6 GHz frequency, so as to enable exchange of estimated values between the UEs and the network, and assumes that APs can be identifies based on the prior knowledge of the orthogonal channels and transmit beamforming codebook. A strategy for assigning codebook entries to the several APs is also proposed, with the aim of minimizing the mutual interference between APs that are assigned the same entry. Numerical results show the effectiveness of the proposed detection strategy, thus enabling one shot fast BA for CF-mMIMO systems.