Born in Verchères, Lower Canada, Maximilien was the seventh child of August Franz Globensky, a Prussian-born Polish surgeon who served with Hessian mercenaries and settled in Lower Canada after his detachment fought on the side of the British in the American War of Independence.
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Globensky was the grandson of August Franz Globensky, a Hessian surgeon who settled in Verchères, Quebec, and the son of Lieutenant-Colonel Maximilien Globensky.