I have requested for a French long term student visa from India. It's a national visa and not a Schengen visa. My question is that can we still go to other Schengen countries on this visa? If not then can we get a Schengen visa from the Indian embassy in France?
Firstly, the Indian embassy in France gives out visas to India. Assuming you're on an Indian passport, this is useless to you. You need to go to the embassy/consulate of the country for which you want a visa - eg if you are going to Egypt, you go to the Egyptian embassy in France.
My belief is that your long stay visa (more than three months) falls under the lawful category for "Stays Exceeding three months":
So on that theory, yes, you can enter the other Schengen states, as long as you follow those time-limited terms.