Changing France Visa from APS to Long Stay Student

[MoneshRaut]

Hello All,
I am Monesh from India currently living in Paris.
I have completed my masters degree in France and have an APS(Authorise Provisionaire de Sejour).
Now I am getting a chance to do an internship in a company, so they are asking for a "Convention de Stage".
For that I contacted a school but they are saying that I need to change my visa status to long stay student.
1) Could anyone advice me if their is a chance of me to obtain a "Convention de stage" without sacrificing my APS Visa.
2) Can a company provide me an intenship without "Convention de stage"??
2) Can I do the process of changing Visa status in France or do I have to apply from my home country(India)??
3) Will I get an APS once I finish my studies since to get a "Convention de stage", I would have to enroll my self again in a school??

Thank you in advance for your feedback and help.

Kind Regards,
Monesh