Inclined to agree with others that perhaps you need to decide where you want to go first and then decide the best way of getting there. In Italy and France, bus and train services are generally good ( I don't know Spain particularly well). And by late October / November you won't be wanting to spend too long out in the country when it turns wet and windy and it goes dark by 5 pm - that's when you'll enjoy cities where not only do you not need a car, but they can be more hassle than help. If you've not been to Europe before, you may be surprised at just how busy some of our roads are, so f you do decide to hire a car then aim for some of the more rural areas for the first day or two to get used to it. For most people the thought of sitting on the other side is worse than the reality!
Nothing beats the flexibility of a car, don't be put off it's not as hard as you imagine. Everyone needs a little adjustment time during which just take it slowly, other drivers will overtake you if they want to. Unlike others here I have no difficulty with gear change or side of the road but I do need adjustment time for orientation using my mirrors, especially the rear-view mirror. I'd advise looking at your mirrors for a while and getting used to actually seeing something in them before setting off.
I've often driven a left-hand drive car in a left-hand drive country which is a double whammy and I'm still alive !
You're just a marvel FCG ... everything you do you're just super at!
How uncharacteristically kind of you to say so.
I personally think some people are just easily impressed ;-)
Have a good holiday !!

I too have always been a bit cautious about renting cars on the continent. But this I did in the south of Italy of all places. And as someone who loathes driving, especially on motorways, who is known as a terrible driving, I was impressed at how easy it was for me to do. I picked up the car in Lecce, so a small city and it just worked for me straight away.
The only issue was the availability of an automatic. Hertz failed to provide the car so waited 3 hours for them to locate an auto, despite the guy trying to get me to take a manual (which I have no idea on). The roads were good and as long as you keep to the speed of the other cars no issue. Better to go for a smaller car than larger for parking and small roads.
Changing driving sides from left to right, or right to left, is individual for everyone and also depends and the place. I made my first trial years ago in Cyprus. I tried and gave up after half an hour. The traffic was chaotic, streets were narrow and it was very hot (no AC in the car). Altogether it was a stressful experience.
Another time I rented a car in the UK and drove across the whole country. Good driving conditions made it much easier to adjust. It took about an hour to make myself feel comfortable behind the wheel. There are a couple of things that can be distracting at the start - rear view mirror and changing gears, and on the road, the roundabouts. But, with good concentration you can get used to the differences in a couple of hours.
Another question is whether you need a car. In all the three countries you'll find train and bus connections. There are places in the countryside that aren't easily accessible by public transport, but then you might decide that those aren't on top of your list when you have only two weeks in each country.

I drove my own car (steering on the left) in England and did nor really have any problems. I also drove a rental car in England and liked that less than my own car. One thing to look out for is the distance between you and the other cars when overtaking. This distance is bigger than you are used to. Be aware of that.
I can't speak for Spain, but I highly doubt any French driving school will give you lessons. You'd have to sign up for the whole package (around €1500, plus a per-hour charge of 38€, plus a fee to take an exam of 300€, which will involve 40 random question out of 4,000 questions from the Code Rousseau - and all in French). If you don't pass it, you have to take more lessons and take it again. Even if you do pass it, it will take months. They're not just going to give it a try and see if you're fit to drive on French roads. Driving lessons are a serious business in France. And even if you could convince some driving instructor to take you on a freelance spin or two (which is close to unthinkable), if he or she didn't approve of your skills you could be reported to the police. Yes, it could be considered draconian, but that's the way it is. I imagine it's the same or worse in Spain.
I would suggest the same in Spain (re driving schools) as given in the post above covering France.
Besides the countries you wish to visit will have some regulations that will not be applicable in others.
Have driven LHD cars in RHD countries and vies versa. Gearboxes:I have a 5 speed car for everyday use and a classic with a 3 speed. Reverse on that is where 1st normally is That is very confusing, maybe worry for the person behind at the lights. Storks on for lights wipers etc can be explained at the pick up point. Newer cars in Europe have day light running lamps which are lit all the time at the front. The rears are only lit when the lights are on. Use headlamps in poor weather conditions.
Keep within the speed limit as cameras are everywhere these days. In Spain we have sections of road marked where fixed ones are located. Mobile ones are not. But then there are phone apps to indicating the latest positions:-)
In Spain do not touch the GPS whilst driving. All countries never use the phone.
Don't ever speed in France, either. There are something like 30,000 unmarked speed cameras now in France. They will send your rental car information to the agency with which you contracted, which will contact the police, who will issue a ticket, which will be sent to your home address in Australia. There are administrative fees of about 30€ for the rental agency to forward your information to the police. The ticket likely won't reach your Australian address for several months, by which time it will have compounded. If you don't pay it (you can online), you may never rent a car in France again (not a certainty, but a possibility). Don't speed, and learn the road rules before you go. And at least in France, never use an app to help you locate speed cameras. That is illegal, as is talking or texting while driving. Police in France do not have to have any probably cause to pull you over, either.
You are required to have an international driver's permit to drive in France as well (likely no one will ask for it unless you are involved in an accident, though).