If so, is there any difference in meaning and the field of use? Can "He sleeps now." be considered grammatically wrong?
Both sentences are technically correct, though the former is a lot better. The latter is a bit awkward to say, due to the irregular way of using the simple present tense.
The simple present tense is used for habitual or factual actions, as in; he works on Fridays. It is something he does, in this time space, though he is not doing it right now.
That is what we use present participle for, things that are happening right now. If set person is sleeping right now, as we are speaking, then I would use the first option; "He is sleeping now". Though, the other option is correct, and could be used to one's advantage, as to perhaps highlight a trait with the person saying it, i.e. that they're a bit social awkward, or that English is there second language. Also, the latter option could even sound poetic, as said by someone siting a legend.
He sleeps now... but one day he shall awaken.
So, there are places one can use the simple present in situations like this. Here's a link if you want further explaining, or if you found my explanation worded badly. http://grammar.ccc.commnet.edu/grammar/tenses/simple_present.htm