I'm about to play CoC for the second time and this time I want my character to have an appropriate movement speed. The first time I played the game was when it had just been released on the PC and I notice very quickly that Jack moved unusually slow. I read on the forum and found someone mentioned that when you have a resolution higher than 640*480, the player somehow moves a lot slower. I ran the game on 1280'*1024 and it was impossible to beat the game, until I found the "svcklead patch" which made it possible to finally beat the game.
Now a couple of years later I'm about to run this game again with the "svcklead patch" installed from the beginning and this time on a resolution of 2048*1152. So how should I set the movement/sneak speed so that Jack doesn't move to fast but at the same time not to slow?

Make your resolution and graphics as lowest as possible, try each option from graphics (low/medium/high etc.) until it runs as smooth as you want it to. It's probably just your video card that can't handle the game so well on maximum graphics and resolution.
Try the 640 resolution to start.

Well it's nothing wrong with the FPS, but the general movement speed of the character that is the problem. My specs are totally capable to handle the technical details. To clarify, what I want is to use the "svcklead patch" to increase the movement speed, but I don't know how much I should increase it so that it doesn't break the gameplay?

Yeah, I understood that part, but it's really weird, if your PC specs are capable of running the game smoothly, you shouldn't need a speed boost and the character must run normally.
I believe you do know how to toggle walk and run right? If that's not the problem I have no idea what to say... either try searching more for the problem, wait for other people's input, or as a last choice reinstall the game. Also be sure your game is not modified and edited by anyone in any way except by the original creators.

svcklead doesn't have any speed parameter settings or anything to set how much speed to give your character as far as I know.
As of a patch, the patch I have found is working just fine, if you'd ever need it, just download it.

The patch that you use is the "svcklead patch". You can change movement speed under "Player settings". I can also say that I haven't start playing the game yet, because I don't feel like going back and forth from the game to the editor. Seems to me that every one who plays this game now days, changes the movement speed and and I just want to know how much?

Back when the game was in playtesting stages, there was a sprint and jog feature. The jog speed is the games current speed. Sadly the sprint feature was removed just before development finished.

If you can figure out a way to edit the XML data (or just use svckleads patch), try changing the walking speed from 380 to 560. 560 was the default sprint speed.