Aigle is a historic town and a municipality and the capital of the district of Aigle in the canton of Vaud in Switzerland. The official language of Ai…Aigle is a historic town and a municipality and the capital of the district of Aigle in the canton of Vaud in Switzerland. The official language of Aigle is Swiss French. Aigle lies at an elevation of 415 m about 13 km south-southeast of Montreux. It is on the east edge of the Rhône valley, at the foot of the Swiss Alps.