Complex sentence: Braudel had already started archival research on his doctorate on the Mediterranean when he fell under the influence of the Annales School around 1938 when he entered the Ecole Pratique des Hautes Etudes as an instructor in history.
Split into simpler sentences: Braudel had already started archival research on his doctorate on the Mediterranean when he fell under the influence of the Annales School around 1938. Also around this time he entered the Ecole Pratique des Hautes Etudes as an instructor in history.