What group of people counqurered gaul at the end of the of the 5th century?

It was the Roman Empire. The Gauls were Celtic peoples that had spread over most of what is now France, Belgium, Southern Germany, Austria and the Czech Republic until the Battle of Telamon (225 B.C.) started forcing them into decline. They were conquered in the Gallic Wars of the 50's B.C. Gaul became a province of the Roman Empire and were culturally assimilated into a Gallo-Roman culture.