I am flying on Alitalia next year from Vienna to Rome and then Rome to Paris. I have heard two conflicting pieces of information on the carry-on baggage. Here is the info I have heard, can you please confirm which is correct?

1) 1 Carry-on bag not exceeding 8kg
2) 1 carry-on bag not exceeding 8kg AND a small bag (purse, briefcase) that can fit below the seat in front of you.

Can someone please confirm which of these is correct? I plan on having a checked bag and a briefcase and small carry-on (36cmx25cmx25cm, or even smaller).

Thanks, the website is somewhat confusing.