Reserve one slice of pineapple for decoration and chop the rest. Cut the sponge cake in half horizontally. Place the halves on a flat surface with the cut surface facing upward. Sprinkle a little pineapple syrup from the tin over each of them.
Place the chopped pineapple in a bowl; add a little whipped cream and mix well. Spread the mixture on one half of the cake.
Cover with the second half. Place the cake on a plate. Spread the remaining whipped cream smoothly over the top and the sides with a palette knife dipped in hot water.
Cut the reserved pineapple slice in cubes and use to decorate the gâteau. Chill in a refrigerator till ready to serve.