As Ahmesis pointed out, Coptic (or perhaps more properly, Egyptian) is an Afro-Asiatic language and is thus not related to Indo-European languages, though some Historical Linguists posit an even older parent tongue which encompasses many of these macro-families including I-E and A-A.
The ancient Egyptians did indeed borrow a few words from their IE speaking "neighbors" - Hittite, Greek, and Latin are/were all IE languages (amongst a few other minor IE languages in the area).
The only specific example that comes to mind is the word for "ox" - I believe in AE it was something like 'akh' (where 'kh' is the 'ch' of German "Bach") - most likely an IE borrowing. The Proto Indo European word was something like "*uks-" - the 'k' became an 'h' sound in many IE languages.
By IE borrowings I'm referring specifically to Ancient Egyptian; obviously with the Hellenization of Egypt, thousands of IE Greek words entered into the language.
There are many words in various langauges that not only sound alike but also convey very similar meanings - it does not necessarily mean the langauges are related in any way.