Dry foods will be no problem with security, and ditto for liquids or gels in the checked bag; customs rules may be tougher - even packaged processed meats and dairy products will generally be banned coming back into the US - including (IME) re-importation of US products. IME, packaged/processed fruit (jam, canned fruit) have been fine, although I've always declared them to be on the safe side.

I'm not sure how European countries handle these things; the US may be a bit stricter than most. Your best bet would be to look at the customs website for your first point of entry into Europe; once there, customs between countries is much less likely to be an issue.