The barrels are an interference fit on the action. Pushing the button does indeed do something, but, there remains more to do. Put on a pair of shoes with a leather toe (bear with me). While holding the Charlin with your non-writing hand, around the center of the barrels/action, and while using the same hand to push the button, put the muzzles into the toe of that leather shoe, and deliver a blow to the center of the buttstock, in a karate chop fashion. The lever will need to be in the up position. If it has been several decades since this was last done, expect some resistance. The gun will sound a little "pop" when the interference has been broken, and you will need to remember to hold the barrels to the action gently at that time. You can then slide the barrels rearward to separate them from the action/stock assembly.
Most Charlins require tools to dismantle the breech, which, is ill advised, in any case, as you stand a pretty good chance of loosing the bearings, or their springs. There is little lubrication or maintenance work that ever needs to be done in there.
The action of the Charlin should open and close almost silently-if you are getting a "clunk, clunk", upon moving the breech block back and forth with the opening lever, you have a broken disconnector spring. No damage will come from using the gun in this condition, but, it should be repaired.
Charlins are nice guns, the trick is finding one that fits. I prefer the Darne R action, but, that is only a personal preferrence. Let us know how it goes, and good luck with the new-to-you gun.


Best,
Ted