This name is a synonym of Fragaria viridis Weston.
The record derives from RJP
(data supplied on 2011-10-18)
which reports it as a synonym (record 26570) with original publication details: Flora gallica Flora gallica; 1806 299 1806.
This name record (from RJP) was not included in version 1 of The Plant List. It is possible the same name was included from a different data source, to check this you can search for Fragaria calycina in version 1 of The Plant List.