Of course. We have learned the present tense from the first lesson. Il paye sa facture. means "he pays his bill" or "he is paying his bill". "En train de" is just a way the French have to emphasize the second form with recent or continuing action.
However--fair warning--duo does not accept the simple present tense for the French version--which I think is mistaken.
(BTW, "payer" is also spelled "paier" with different spellings of the verb conjugations.)
I disagree. He is "just now paying" his bill can carry the implication that he was slow to pay or in arrears, which is not present in the French. And with bills (plural) it seems more like "in the process of paying" which might mean a process of weeks or months. "They're just now paying the bills for her emergency surgery."
Well, it really depends on the context. The English present continous "he is paying" is not strictly used for the present since it is also used for planned activities (e.g. "I am attending a meeting next week") which is quite close to "il est en train de payer", while "He is going to pay" is always used as closer/planned future as far as I remember. In my case duolingo system refused my translation of "Il est en train de payer" into "he is going to pay" which, again, I think it is an error.