We would need a few more details to answer your query. You can definitely use Open Type fonts in InDesign, please check out this help article for more details: Use fonts in InDesign.
Same problem, when clicking on the O symbol in order to applicate an alternative style, this message appears "Les propriétés Open Type ne sont pas applicables" in French. (Open type Properties aren't applicable) Impossible to acces alternatives versions of glyphs (which actually appear in the dedicated window). The same font perfectly works on illustrator.
Cela signifie que dans la police utilisée, il n'y a pas de variantes OpenType : pas de ligatures conditionnelles, ou pas de glyphes alternatifs, etc. Mais ça n'empêche pas de l'utiliser. Quelle est cette police ?