The striker drilled home a volley from 12 yards in the 39th minute to clinch a 2-1 victory and top spot in Group B of the tournament.
The Young Lions now take on Greece in the semi-finals in Tallinn on Thursday.
John Lundstram of Everton opened the scoring for England in the 16th minutes and Harry soon forced a fine save from Jonathan Millieras.
However France, who had won two out of two before Monday, levelled through Jordan Veretout in the 31st minute.
Eight minutes later and Harry fired home what turned out to be the winner, volleying into the bottom corner after Millieras punched out Robert Hall's corner.
Harry had one further effort in the second half before being substituted six minutes from time.