I have a French Swamp from 1996 with no expansion symbols and white borders. It's from Dan Frazier and has one of the Beta arts. I'm left puzzled because 4th edition was in 1995 and the fifth edition in 1997.
It sounds like it's from the Introductory Two-Player Set (Rivals Quick Start Set in the U.S.), it was a white-bordered set released as a quartet of preconstructed decks intended to introduce players to the game and was released July 1996.
The contents of the Introductory Two-Player Set vary according to their edition and language. All versions with the exception of the Japanese release have in common, however, that the cards used to build the preconstructed decks in there are unique. They look similar to Fourth Edition cards, but feature a 1996 copyright date and in some cases reformatted text.
From the Magic Rarities page on the subject: