Theme Horse

Hi Baptiste,

Yes you have to set up or migrate each and every settings of widgets and customizer only and you can migrate it easily via these two plugins.
Customizer Import/Export Widget Import/Export Plugin
First activate the free version theme and upload/activate above plugins and you will find Export/Import option at the bottom of the Appearance > Customizer for Customizer’s data and settings and for Widget’s settings and data just go to Tools and you will find Widget Importer & Exporter option. Just export both settings then activate the pro theme and import it via under same option.

If you can not import just let us know and we will help you to import those data and settings to a pro theme.

Thank you!