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."