I'm living vs I live

[angelene001]

The situation is:
I'm on an exchange programme in France. I'm staying here for 6 months. [or I stay here for 6 months?]
a) I live in Paris.
or
b) I'm living in Paris.

Which is the correct option here?
Should I use present continuous because it's something temporary?
Is present simple a grammar mistake here?

 

[bhaisahab]

Use the continuous in both cases.

 

[5jj]

Should I use present continuous because it's something temporary?

Continuous forms are normally appropriate when the situation is of limited duration.

Is present simple a grammar mistake here?

Yes. It suggests that Paris is your home.

 

[angelene001]

What about "to study + name of the subject"? Is it usually treated as something of limited duration?
We are studying biology at school. --> school education has got a limited duration
I'm at university, I'm studying maths. --> university education has got limited duration

 

[5jj]

"I am studying X" is appropriate for students. However, an academic might well say "I study X", because this is his/her full-time work.