You can cook eggs in a copper pan but the heat transfer is not as fast as it would be with the regular pans.
It's best to cook the eggs in a non copper pan for best results but you can cook the eggs in the copper pan if you want too or need too.
I would make sure you got the copper pan hot and add some butter or oil to the copper pan to keep the eggs from sticking.
If you don't put any butter or oil into the copper pan then the eggs will likely stick.
But I've never had a problem with the eggs sticking to a copper pan when I use some butter or some cooking oil.