As your main purpose in visiting is to study, it would appear that the Short Term Student Visa is appropriate. The guidance for the Standard Visitor Visa says study cannot be the main purpose of your visit.
You need a visa to complete an internship in France. The visa you need depends on the duration of the internship. In your case, you need a short term visa since your internship lasts less that 90 days:
This type of visa is generally issued for tourism, business trips or family visits.
It is also issued to persons entering to ...
You are going to have problems.
As Giacomo Catenazzi says, selling a property to pay for your trip is a bit of a red flag. In fact any large amounts of money suddenly appearing in your account, or the account of someone who is paying for your trip, is going to be a red flag. You have to make sure that your documentation of the sale is rock solid - a legal ...