If you're looking for French classics, I would recommend Darboux's Théorie générale des surfaces There is a lot of analysis there. In fact the text is mostly about the interplay between differential equations and differential geometry. Goursat's Leçons d'analyse are also quite nice. I read somewhere that Bourbaki started as a rejection to this text, but that only makes it more interesting. I also like Appell and Goursat's Théorie des fonctions algébriques et leurs intégrales. Appell's books on mechanics are really nice as well.