Without rejecting @jlliagre interpretation, which I find convincing, I must say I never understood that sentence that way. I've always understood les eaux in Perrault's text in its medicinal meaning. Eaux as in villes d'eaux, the English "spa", the German Medizinische Bäder.
In Charles Perrault's times (17th century) aller aux eaux or prendre les eaux meant aller faire une cure thermale.
These are not much used nowadays, or used between brackets1, but we can still find the phrase in dictionaries.
Les eaux : les eaux minérales d'une station thermale. Aller aux eaux, prendre les eaux, faire une cure thermale. Une ville d'eaux. (Le Robert)
Although English prefers the word "spa", when translating a text from French, "take the waters" is a common translation.
I was first going to the Pyrenees, to take the waters of Cauterets; (The Memoirs of Chateaubriand).
The sentence in the question is the exact wording2 of Perrault's, not an adaptation. The translations into foreign languages are often very loose, but when translations stick to Perrault's text, the medicinal interpretation is retained - at least for those I know.
They went to all the waters in the world; vows, pilgrimages, all ways were tried and all to no purpose. (18th century translation by Robert Samber and J. E. Mansion)
Sie reisten in alle Bäder der Welt, legten Gelübde ab, machten Wallfahrten. (1921th century translation by Hans Krause)
1Quand on « allait aux eaux » à Vichy.
2 But the punctuation has not been reproduced correctly. The original text has a semi-colon in place of a colon.