This answer is largely based on the Movies & TV post which user1964 linked in a comment.
Yes, Poirot was a religious Catholic.
In the story Murder in Mesopotamia (Internet Archive link), he mentions twice that he is a "practising Catholic":
Then he said quite irrelevantly: ‘An interesting man, that Father Lavigny.’
‘A monk being an archaeologist seems odd to me,’ I said.
‘Ah, yes, you are a Protestant. Me, I am a good Catholic. I know something of priests and monks.’
‘I had a lengthy conversation with Father Lavigny. I am a practising Catholic and I know many priests and members of religious communities. Father Lavigny struck me as not ringing quite true to his role. But he struck me, on the other hand, as familiar in quite a different capacity. I had met men of his type quite frequently — but they were not members of a religious community. Far from it!’
In the later story Taken at the Flood, he even enters a Catholic church to pray:
Moved by an impulse Poirot went through the gate and along the path to the door of the Roman Catholic building.
He removed his hat, genuflected in front of the altar and knelt down behind one of the chairs. His prayers were interrupted by the sound of stifled heartbroken sobs.
His religion is not mentioned in earlier Poirot stories, but it's one of the things that helps to fill out, at least a little, the background of the character. Although he doesn't frequently refer to his religion, he also doesn't (as far as I know) say anything which contradicts him being religious: it's just not usually mentioned but occasionally comes up.