Coeck studied at the Royal Academy and at the Higher Institute of Fine Arts in Antwerp, under Albrecht De Vriend, the teachers Rogier and Piet Verhaert and Pieter Van Der Ouderaa.  Coeck was appointed director at the drawing schools iin Wilrijk in 1900 and in 1908 in Niel. During WWI. Coeck moved to the Mediterranean, France from 1915 to 1918, where he met Count Louis de Montalbo, from San Marino, and for which he carried out a number of assignments. After the armistice, Coeck returned to Belgium. Yet he regularly returned to Nice, Monaco,San Remo and Menton.

Coeck made a name for himself with the portrayal of his fellow villagers and the depiction of village and regional views.