Françoise is the feminine form of
François. It is not a diminutive, as it does not contain any of the known French diminutive suffixes:
https://en.wikipedia.org/wiki/List_of_diminutives_by_language#French (in English)
Francine is one of the diminutives of
Françoise, as it contains the French feminine diminutive suffix
-ine.
A woman's legal name does not necessarily need to be
Françoise in order to justify calling her
Francine in everyday life. Sometimes diminutives become independent names (see the links below), and eventually people forget that the name started out as a diminutive. Such names can then get diminutives of their own, e.g. Francinette for
Francine.
•
-eau: https://www.behindthename.com/names/usage/french/pattern/*eau (this diminutive suffix is unisex)
•
-elle: https://www.behindthename.com/names/usage/french/pattern/*elle•
-ette: https://www.behindthename.com/names/usage/french/pattern/*ette•
-ine: https://www.behindthename.com/names/usage/french/pattern/*ine•
-on: https://www.behindthename.com/names/usage/french/pattern/*on (this diminutive suffix is unisex)
•
-onne: https://www.behindthename.com/names/usage/french/pattern/*onne (this diminutive suffix is strictly feminine, but very rare)
•
-ou: https://www.behindthename.com/names/usage/french/pattern/*ou (this diminutive suffix is unisex)
Sometimes a masculine name does not have a proper feminine form, in which case people simply add a feminine diminutive suffix to it in order to make it feminine.
Charlotte is a good example of this, although I would say that technically, it is a feminisation of
Charlot, a medieval French diminutive of
Charles.
https://en.wikipedia.org/wiki/Charlot_(name) (in English)
https://en.wikipedia.org/wiki/Charlot (in English)
Forchta in biuonga quamon ouer mi, in bethecoda mi thuisternussi.
In ic quad: "uuie sal geuan mi fetheron also duuon, in ic fliugon sal in raston sal?"