This can be easily achieved by configuring Experience Manager accordingly to your needs.
Just follow these steps to configure everything as needed:
Configure General Content to be created in publication 02 Global
Content. This is done when you create the Content Type (in
Experience Manager terminology).
Configure the French Website Publication to have localized content
created in 03 French Content. This is done from the Dashboard -
Settings - Blueprint Context Settings - 03 French Content
Publication, as shown in the red box in the image below.
Now, any localization done in the French Website will be stored in the 03 French Content. However, any content type that is created from this same website will be stored wherever that content type was configured to be stored.
Follow these steps from Experience Manager to get the content in the publication you want it:
To create content in 02 Global Content, just create any content from
Experience Manager and this will be automatically stored in 02
To create content in 03 French Content, from Experience Manager
create content and then localize it, this will be automatically
localized into 03 French Content. All the configuration can be done
from the Experience Manager Dashboard settings, you need to uncheck
the check-box that says "Also create components in this Publication"
With this set up, you can accomplish just what you want. I have tested this myself to make sure I don't mislead you.