This game appears to use ScummVM and therefore should be playable in Linux. (I am referring to the original version, not the director's cut.)

However, [url=http://wiki.scummvm.org/index.php/Datafiles#Broken_Sword:_The_Shadow_of_the_Templars]http://wiki.scummvm.org/index.php/Datafiles#Broken_Sword:_The_Shadow_of_the_Templars[/url] gives a list of the files necessary for ScummVM. These files don't match the files that are provided. For instance, there's no SMACKSHI folder and the speech files are named .clv, not .clu.

Is there anyone who has actually managed to run this in Linux (or otherwise using a ScummVM for another platform), and how did they do it?

Hi, The reason the speech is named .clv is because GOG are using recoded audio, By this i mean the original game used WAV format and this made the speech files really big in filesize, so they compress them by converting them into a different format using ScummVM Tools, the .clv is fully supported by ScummVM so you dont need to worry about the file extension being different the audio will still work the same.
The reason there is no SMACKSHI folder is because the GOG version was made before the Smack video's where supported by ScummVM so they used the old DXA video's which can be found in the video folder of the GOG version,
And lastly i have had Broken Sword 1 run in linux a few years ago, haven't tried it since but it should still work, if you need any help let me know, but all you should have to do is Install scummvm and direct it to the broken sword folder to find the game.