Can I apply for multiple visas?

Hello. I did two years of PVT, then three years as a student, now living in France with a private/family visa.
I do not know if you can apply for two visas, I think the best way to find out would be to call the embassy directly. However, I also don't think it really matters, because - by the time you apply for university and get accepted, it will be a couple months from now. And I think in a couple months you will know if your employer has started or not the formalities of getting you a work visa. If he hasn't... go for uni
When you say you want to get a student visa then change it to a titre de séjour, what type of titre de séjour are you thinking of??
Because I am not sure I understand your second question. Why do you want to apply for a titre de séjour right away? You will get a one year student visa, then at the end of the year if you are still a student and have the proof of enrollment and sufficient ressources etc etc for the following year you will get a one year (or two year depending on the length of your uni program) STUDENT titre de séjour. This only stays valid as long as you are a student, once you are done your student titre de séjour doesn't let you stay in France.
Hope that helps, sorry if I misunderstood the question.