You're right, even in the staircase area, when looking towards the street, it looks like you're inside the Louvre pyramid. It looks like a cathedral because perhaps they wanted to recreate the architectural environment, which at the time of construction, the most emblematic buildings were the church of San Francisco and the residence of the Jesuit priests.
Tienes razón, incluso en el área de las escaleras, al mirar hacia la calle, pareciera que estás dentro de la pirámide del Louvre. Parece una catedral porque quizás se quiso recrear el entorno arquitectónico, que en el momento de la construcción, las construcciones mas emblemáticas eran la iglesia de San Francisco y la residencia de los curas jesuitas