Last year, Boisson entered Roland Garros ranked 361st in the world but battled to the last four. She then won on clay in Hamburg to enter the top 50 before her progress was derailed by injuries.
On Tuesday, Kalinskaya dominated from the start, breaking the 23-year-old Boisson's serve in the first, third and fifth games. Boisson managed a break of her own in game four, but it was not enough.
The Russian broke twice again at the start of the second set as she cruised to victory in 1 hour and 19 minutes on Court Suzanne Lenglen.
She will play qualifier Alina Korneeva in the second round.