Yes, if you know French will find definitely much easier to get to grips with Italian vocabulary than a Russian speaker who doesn't know French would find it. This is certain. They are both Latin languages, and a large proportion of the vocabulary is similar or from a similar root. Of course, they are different languages, and they are not mutually comprehensible. Daniel, as a native Italian speaker, says that he can't understand spoken French. Likewise, most French speakers couldn't follow a conversation in Italian. However, if a monolingual French speaker tried to read the front page of an Italian newspaper, a Swedish newspaper and a Czech newspaper, for example, he or she would probably be able to make out a reasonable amount of what was written on the Italian newspaper, while they would most likely understand nothing on the Swedish or Czech one. The same would apply for Spanish or Portuguese - knowing one Latin language gives you a headstart in when it comes to understanding the vocabulary of another Latin language. As Andrew says, knowing French won't help you form an Italian sentence. It won't help you pronounce Italian or carry on a conversation in Italian. But you will certainly have an advantage over people from your country who have never learnt French.

If you already know French, guessing at the meaning of Italian words would give you a better score than not knowing neither French or Latin, especially when reading. It would not help much when producing your phrases in Italian. Anyway I would suggest you to discover and study at an early stage the list of so-called 'false friends' (faux amis) between French and Italian languages (a search over Internet would probably do).

I don't think so... I mean, I am a native Italian speaker but I don't understand what French people say. If you still know French then you can learn Italian easier because you know how to approach to a new language. It would be the same for German, Spanish etc.

YES! Last year, I went to Italy for a month with my family and could get the gist of what the Italians were saying thanks to the similarity between French and Italian words.

Basically yes, French and Italian share several grammatical structures (they're both neolatin languages) and a huge quantity of words have a common origin. Reading and understanding the grammar will come a little easier, but speaking is a different story. In Italian we pronunce every letter in a word (only the "h" is generally mute), meanwhile French has many exceptions.