Opening disclaimer: This answer is based on personal experience and things I was told at the time, which was in the UK, not from India, and was for a different long-stay visa than yours.
At the time, my long-stay visa was very delayed. I was told that there is nothing I could do besides wait. In my case I started work about 3 weeks late. They will email or text (if you sign up for this option) you when your passport is ready to be collected, and they will not specify whether the visa is accepted or rejected. You find that out when collecting your passport, which in my case could be done in person or in the post.
If you're really in a pinch, check whether the website you used to start your application has a 'Contact Us' page. You can send an email and request that they call you. They will, sometimes, call you back after that.
NB: I was told by the agent that long-stay visas are sent to France (Nantes, IIRC) and processed there. So at some point, to the company, the process becomes a 'black box' and they won't know anything once it's sent, until it arrives back. Note also that the month of August is very slow in France, if you're aiming for around this time.
Another poster on this SE had good results getting their university/lab to contact the visa office, but they were a researcher, so this may be less of a valid option for you.
If you have gotten to this point already, I would imagine it's quite unlikely that you will be denied. The company has already vetted your application, so it's looking good.