When burning wood in a wood burning fireplace it's normal to have a slight smell of smoke coming into the house especially when you first light the fireplace.
And it's normal for some fireplaces to smell like smoke a little bit when burning but you should not smell a lot of smoke smell coming from your fireplace.
A normal and proper operating wood burning fireplace is supposed to send the smoke smell outside the house through the fireplace chimney.
You could have outside air being sucked into the room somehow so I would get the chimney checked out by a fireplace expert or chimney sweep to be sure the chimney is clean and working properly.
Sometimes it's possible that a chimney may not be installed correctly or sealed properly allowing air to be sucked into the house.
I get a small amount of smoke smell coming into my house when lighting the fireplace and for a little bit while it's burning but after a few hours the smoke smell goes away.
You shouldn't smell a lot of smoke coming into your house and if you do then something is wrong.