Morning is a common English word, as you know. Forenoon, on the other hand, is so rare that I'm not sure many native speakers of English will even recognize the word.
How rare is it? To find out, I searched the Corpus of Contemporary American English (COCA) for both morning and forenoon. Here are the results I got:
Search term Number of results
-------------------------------------------
morning 128954
forenoon 16
That makes morning roughly eight thousand times more common than forenoon. It's safe to say you should stick to morning and avoid forenoon entirely.
But wait! Is it possible forenoon is only used in dialects of English other than US English? To find out, I searched the Corpus of Global Web-Based English (GloWbE), which contains samples of English from twenty countries. And in none of those countries was it substantially more common than in the US; the numbers in every country were less than one occurrence per million words. And the few results that I do find are mostly in fiction.
So yes, it is safe to say: avoid forenoon. Use morning instead.