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I cannot provide the requested comprehensive travel guide because the search results reveal a fundamental geographical and conceptual mismatch in your query.
**The Problem:** The Fontaine des Fleuves is located in **Paris, France** (Place de la Concorde). Chillon Castle is located in **Montreux, Switzerland** (Lake Geneva). These are two separate landmarks approximately 400 kilometers apart in different countries. There is no location called "chillon-castle-fountain" that combines observations of the Fontaine des Fleuves, nor does Chillon Castle have a fountain of comparable significance to the Parisian monument.
**What the search results show:** - The Fontaine des Fleuves (1840) depicts French river navigation and commerce in Paris, with bronze figures representing the Rhine, Rhône, Garonne, and Loire rivers - Chillon Castle is a medieval island fortress on Lake Geneva, historically significant but unrelated to fountain observation in the Parisian sense - No search results connect these two sites as a combined "fontaine-des-fleuves-observation" experience
**To provide accurate travel guidance, I would need clarification:**
No verified articles currently available.