I also found on his Leaflet.GeoJSON.Ajax repository a great example and data of refuge in the Alps. Exactly what I am actually looking for. I adapted little things of his pretty complex code to fit to my wish and thanks refuge.info and his contributors (“Les contributeurs de refuges.info”). They created a great API allowing the public to freely use the data of their website.
You will have then 2 new layers available:
POI - Refuge.info POI