The answer is: sure! Go straight to your embassy in Vienna.
indeed, since you say you are "living in" .AT, that is where you should go. (If you went to the Paris one, they might just tell you - oh, go to the Vienna one since you're living there.)
"Issue of a duplicate passport, in case passport was lost, stolen or damaged (with 36 pages)
If an Indian national who is legally resident in Austria has either lost, damaged his/her Indian Passport or the passport has been stolen, he/she is required to approach the Embassy of India, Vienna to get a duplicate passport. A duplicate passport, just like a new passport, is valid for travel to all countries and is valid for ten years.
If an Indian national who is on a short visit to Austria and his/her Indian passport is lost, stolen or damaged within the period of validity of his/her Austria/Schengen visa, the individual is required to approach the Embassy immediately for a travel document. Such individuals would be issued a short validity passport as they may not remain in Austria for 30 days, which is the time generally taken for preparing a full validity passport.
In case an individual on a short visit to Austria loses his/her passport and is unable to pay the requisite fees and wants to depart for India urgently, an Emergency Certificate is issued to him/her which is valid for return to India. Emergency Certificate issued to an Indian national by the Embassy does not validate travel to any other country and is meant for one way travel to India only.
A Short Validity Passport is issued for a period of six months only in the cases when the Embassy finds it necessary to issue such Short Validity Passports.