This specific WMTS source has a small problem: not all reported scales have available tiles.
If you look at the capabilities document, the TileMatrix has 22 scales available (up to level 21) for the layer
Photographies aériennes. QGIS will try to fetch tiles up to the level 21. That is what you have in the capabilities document.
If you install the QGIS Network Logger plugin, you can check for yourself that QGIS is able to fetch tiles up to level 19.
If you zoom more than that, QGIS will try to load new tiles from level 20, instead of scaling the tiles from level 19. But the server does not deliver tiles at level 20 and 21 (I've added a screenshot of the 404 errors). Maybe these levels are only available for authenticated users.
If the capabilities reported just up to level 19, you would be able to zoom in and get pixelized tiles beyond that. But with this server, QGIS will try to fetch more detailed tiles, instead of zooming the previous ones.
You can use MapProxy to provide a WMTS service with just the scales you are able to get from IGN.
The result will be a WMTS server providing the correct metadata to QGIS. After level 19, QGIS will scale the image, as you can see in the image below.
To configure MapProxy, you have to provide the list of scales, without the last two. You can get the scales from the capabilities or from IGN documentation.
The configuration will include:
- name: photographiesaeriennes
title: Photographies aériennes
I've tested this MapProxy configuration and it works. The exercise should be improved to handle all layers and different girds, if you need so.