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Florian Thauvin came close for the hosts early on, but his effort was comfortably saved by the keeper.
The visitors doubled their lead two minutes later when Kane arrived at the back post to tap home Ince's cross on the line.
Nathan Redmond almost grabbed a third soon after, but after working some space on the edge of the box, his fierce drive was parried by the keeper.
With a minute left in the first half the hosts were back on level terms when Sanogo slotted in Paul-Georges Ntep's pass from close range.
France started the second half on top and Jordan Veretout threatened with a low drive from range that whistled just past the post.
The hosts continued to put England under pressure and Sanogo lashed a strike off target, before Tiemoue Bakayoko's deflected shot went narrowly wide of the far post.
In the 73rd minute France finally made their dominance pay by scoring their third of the evening, as Kingsley Coman fired a strike into the top corner.
France threatened to add a fourth late on, but their three goals proved enough to bring England's unbeaten run to an end.