Complex sentence: Leaving America at the end of 1945, she arrived back in France in January 1946 to take up the position of professor of "accompagnement au piano" at the Paris Conservatoire.
Split into simpler sentences: Leaving America at the end of 1945, she returned to France in January 1946. There she accepted a position of professor of "accompagnement au piano" at the Paris Conservatoire.