Park along the small road, next to the sign indicating the hot spring on the left-hand side or a little before it.
This route is marked by the Club Vosgien from the Reherrey car park
(S/E). Follow the path down the steps to the hot spring.
(1) Cross the stream and continue downhill to the village of Reherrey. Cross the bridge and take a first turn left then right to reach the car park where the hike starts.
Follow the blue triangle markings to the ponds.
(2) Cross the bridge at the end of the car park and turn right, following the Ravage stream. Reach the Pont du Rondin bridge by descending slightly to the right of the main path.
(3) After rejoining the trail, turn right and continue to a forest path.
Red Cross markings
(4) Continue left to the Étang de la Besace lake and go around it on the left. Keep left for about a hundred metres.
(5) Take the path on the left towards the Grand Étang.
(6) At the end of the lake, turn right. Pass a beautiful house on your left and reach the next intersection (house opposite below).
Blue Cross signpost
(7) Turn left towards Pré Grandemange.
No more markings
(8) Go down the forest road on the left to the Reherrey car park.
(2) Follow the same route back to the starting point of the hike (S/E).

The second half was more traditional, but also very pleasant. Definitely worth doing! (I just noticed a small error on the map for the last part, but it's only in the explanation, so it wasn't a problem.)