You cannot obtain a regular long-stay visa from within France but you don't necessarily need to go back to Australia to transition to a long-term status. There are at least two solutions you could explore:
Applying for a French visa from another European country. Channel hopping at the end of the procedure is not enough, you need to be a resident/have some sort of long-term status and proof of address where you apply. But you could try something like a working holiday visa in the Netherlands to save you the trip back to Australia and discover another European country. Be aware that the application can take several months.
Applying for a carte de séjour directly. The rules are complex, students can do it under certain conditions for example (see https://www.service-public.fr/particuliers/vosdroits/F15898) and it's also possible for a vie privée et familiale permit (partners of French citizens) no matter your current status. I am not sure whether it's allowed in this particular case but you do have a long-stay visa already so it might be worth a try.
It's important to try to switch status before the expiration of your current visa. Once it's expired and even if you are staying perfectly legally on the visa-free Schengen allowance, you won't be allowed to apply for a carte de séjour as worker.
If the problem is that returning to Australia is inconvenient right now, do note that, as an Australian citizen, you may stay in France for 90 days at the end of the visa, under the regular Schengen short-stay regulations. However, you cannot work during this time. See this question on the travel website for more on this.
Finally, a bit of bad news: even if you do return to Australia to apply for the visa, it's important to realize that having a sponsor does not guarantee that you will get it. The authorities can rule that enough local candidates (EU/French citizens or residents) are available to do the job. So your prospective employer should be careful to describe it in a way that suggests that you are especially qualified to do it.