The francium atom is considered as a prospective candidate system to search for the T,P-violating electron electric dipole moment [Aoki, Quantum Sci. Technol. 6, 044008 (2021)2058-956510.1088/2058-9565/ac1b6a]. We demonstrate that the same experiment can be used for axionlike particles (ALP) search. For this, we calculate electronic structure constants of the ALP-mediated interaction for a wide range of ALP masses. Using the recently updated constraints on products of ALP-electron and ALP-nucleon coupling constants, we show that contribution of considered interactions corresponding to these constraints can give significant contribution to the atomic electric dipole moment. Therefore, obtainment of stronger restrictions for ALP characteristics in the francium atom electric dipole moment experiment is possible.