Do bank in Australia operate with IBAN?

No, IBAN is used exclusively by European banks. To transfer to/from Australian institutions you need to obtain a SWIFT code from your bank.

Would be nice if someone could give example of how to complete transfer on line info.

French bank details mention:

Name of account holder

IBAN

BASIC ACCOUNT NUMBER

The account in Australia gives me a BSB number and an account number.

Australian banks do in fact operate with IBAN numbers when dealing with overseas banks.

According to Westpac - your IBAN number in Westpac is 12 digits - your BSB and your Account number all together. This is typed in without any spaces or dashes.

In addition, most foreign banks want a SWIFT code (your Australian bank will gladly provide one.) Some foreign systems also want an alphanumeric code as part of the 12 digit IBAN - Best to confirm with the foreign bank on that one.