Australians/Melburnians included are generally regarded as being an open and warm people though generalising is always a danger and here too in Australia you can have self centred people disrespectful of others.

I think it is safe to generalise that you can have good and bad people wherever you go, and even in country areas where people are usually even more easy going.

One thing for sure, Australia, Melbourne included is of a great multi-cultural mix and you will be able to experience foods of many nations and you will see people descendant from many different countries, and all getting along in reasonable harmony.

Melbournians are very keen on sport too and particularly the national football game of Australian Rules Football - Season 2008 - Official Website of the Australian Football League and it is very different from what the french would know as football.
If you get to Australia early enough in September you would have a chance of possibly seeing some seasons finals matches, a great spectacle at the Melbourne Cricket Ground (MCG), also home to Football, and then there is the Spring Horse Racing Carnival with racing at various venues and generally a party atmosphere during later October and early November.

So yes, September/October is a good time to come with the colder weather having been shrugged off and people in a vibrant extroverted mood.

As for going to the unknown, many backpackers head to Australia each year from many different European and other countries and so you are certainly not going to be alone and if you want to travel about the country, you will find many doing that.
You could look at staying in a hostel initially and you would meet many people that way.
Have a look at BUG*- Backpackers Ultimate Guide to Australia and YHA Australia re hostels and travelling info.