The frequency dependent polarizabilities of the francium atom are calculated from the available data of energy levels and transition rates. Magic wavelengths for the state insensitive optical dipole trapping are identified from the calculated light shifts of the 7 s 2S1/2, 7 p 2P1/2,3/2, and 8 s 2S1/2 levels of the 7 s -7 p 2S1/2 2P1/2,3/2 and 7 s -8 s 2S1/2 2S1/2 transitions, respectively. Wavelengths in the ultraviolet, visible, and near infrared region are identified that are suitable for cooling and trapping. Magic wavelengths between the 600-700 nm and 700-1000 nm regions, which are blue and red detuned with the 7 s -7 p and 7 s -8 s transitions, are feasible to implement as lasers with sufficient power are available. In addition, we calculated the tune-out wavelengths where the ac polarizability of the ground 7 s 2S1/2 state in francium is zero. These results are beneficial as laser cooled and trapped francium has been in use for fundamental symmetry investigations like searches for an electron permanent electric dipole moment in an atom and for atomic parity nonconservation.