Gurjinder (14th minute, 44th) scored twice while Mohammad Amir Khan (30th) and Rupinder Pal Singh (52nd) found the net once for India. For the hosts Baumgarten scored the lone goal in the 21st minute.
India had earlier defeated France 2-0 in their opening match of the tour.
India went for goals from the onset and opened the scoring in the 14th minute through a penalty corner conversion from Gurjinder.
Thereafter, France had bright chance to take from a penalty corner but Kothajit Singh made a goalline save to deny the hosts.
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India attacked from both the flanks and in the process found its second goal when Amir scored from a rebound after the initial try from the penalty corner fell before his sticks to help the visitors take a 2-1 lead at halftime.
In the third quarter, India goalkeeper PR Sreejesh stood like a rock to thwart a coule of efforts from the Frenchmen.
India continued to show their supremacy and scored their fourth goal through another penalty corner conversion, this time from the sticks of Rupinder in the 52nd minute.
India will play Spain in their next match of the Europe tour at Sant Cugat del Valles on August 10.