Amazingly, the answer is almost a yes. The world record for the lowest parachute jump is only 29 meters, although this obviously involved an already deployed parachute in some fashion (I only found the record, not how it was performed.) This would be problematic but not utterly impossible for your trebuchet jumper. Since your jumper would have a horizontal velocity he's going to need a bit more distance but I don't know how much more.
There was another answer who thinks he won't survive the launch but I disagree--since a trebuchet works by a counterweight rather than a spring there's simply a high acceleration, not a huge spike as the spring releases. You can lower the force by increasing the size, if it's big enough the jumper survives.
However, I don't think medieval technology could build a parachute anything like as good as a modern one. How much worse I don't know.
Now, if you want to make it even lower I could imagine a cold-gas rocket assisted deployment. I have a hard time picturing that being even remotely reliable with medieval tech, though.
Note, also, that it's going to be a very dangerous jump no matter what. The jumper will not have any control over their landing spot or time to prepare for a less than ideal landing and most things they might be landing on will be pretty hard.