Carnets is a Jupyter notebook. It runs entirely locally, on your iOS device. It does not need a network connection.
Carnets does not collect any data, period.
The user can create notebooks and other files, which will reside in the application directory, and can be moved outside of the directory as needed by the user.
During the TestFlight phase, if the application crashes, a crash report can be sent to the developers. This crash report will contain information about what caused the crash (functions being called, values of variables).
The owner of the application, Nicolas Holzschuch, does not have any way to access the data created by the user.