Hey Mathilda ,
Try booting into the recovery partition and "reinstall" macOS. It wont destroy any of your data (programs/files/etc), but it'll reinstall the main operating system files if it's done correctly.
To access the recovery partition, shut down your computer, press the power button and hold down either Option + Command + "R" or Shift + Option + Command + "R" right after you hear the startup chime. In there, select "Reinstall Mac OS El Capitan" and follow the procedures.
Whatever you do, DO NOT go into Disk Utility and reformat your drive; that will delete everything off of your main partition!
Let me know what happens.