SuperSakura is a free, open-source visual novel engine that can run quite a few old games, mostly published by JAST, one of the first developers in the field. In addition to well-known localised titles, Japanese companies produced lots of fairly good games in the 90's that were never translated.
This engine and accompanying tools can be used to convert and run such old games on Linux or Windows. SuperSakura also supports enhanced graphics and a more modern user interface, and has tools to help localise the games.
Note, that SuperSakura is only an engine. The games themselves are under copyright, so they can't be distributed with the engine. You'll need to use the included Decomp and Recomp tools to convert the original game files to a SuperSakura data file. See the readme file for details.
You can build Linux binaries yourself easily from the sources. The engine depends on SDL2, so you have to get that too.
Although a number of games are playable, a few key elements have not been implemented in the engine, including saving and sound. The engine will become more capable over time.
You may want to check out the clever visual novel porting team, SakuraSoftFan Group. They have a lot of classic visual novels that you can run directly in your browser thanks to the miracles of HTML5/JS, including some non-localised games. Very impressive!