If you want to keep the French have a look at the Killarney Heights school on the Northern Beaches, they have a francophone section. Otherwise, you will have to go to the opposite direction and look at Maroubra on the South shore.
I live in the Northern Beaches and I have lived in Switzerland and remember very well the 9 swiss francs water bottle at restaurants !!
IF you come on a 457, you will receive it as well and be allowed to work. As PP said, you will have to pay for the public schools. The rate is $5000 right now. The rent is high. Not sure I would describe it as way cheaper than Switzerland, but the Northern Beaches are expensive. Maroubra is cheaper.
I took me a while to make friends to make honest. Before coming here, we were posted in Barcelona and it's different.
One word about the health cover. Very different from the swiss private one. With 457 you will not be entitled to the Medicare system, so you will need a private cover but beware, event the super platinum cover will only cover you for what Medicare would have given you, not the gap. Australians and permanent resident have private covers that fill this gap. For example for surgeries you would still have thousands of $ to pay. The platinum parts covers for dental with a maximum at around $1000 per year which seems a lot but normal check+hygiene and maybe an X-ray on one tooth will be $460 at my dentist, so for major works be well prepared! Also overs for physic, glasses, ....
You will need two cars. Unless you live in the cbd.
I like the beaches on the north shore more. Houses are also bigger here. Not sure if I would bother with a pool because unless it is heated or very well exposed, you will use it less than you think if you get a "bad" year. Last year was so wet and cold! This year has been very warm, even the winter. But nights are quite cool, so even during the hot months, the water temperature of the pool would be quite chilly as it drops during the might. A true pain to clean it as well, especially if you have a gum tree near by. Even if you have a pool maintenance contract you have to clean it every day in summer.
For the sharks, unless you are crazy enough to swim in the harbour, they will not be a problem on the Sydney beaches. Spiders and snakes, that's another story. Don't rent a house near the bush or in the bush and the number of snakes you will get is near to zero. Spiders, have the house treated by pest control and you will be fine. If you have a dog, you must be very careful with the Australian paralysing tick, deadly for dogs. If taken on time, you can treat and save but you will have to pay $$$$$$. There are preventive measures and you MUST check your dog every night, everywhere (between toes, eyelids, ... I mean everywhere!)
Should you stay or go? for two years only and with kids so young, I would say yes. But I go back every six months. Our package includes one trip to Europe per year, we pay for the second one.
Company also pays house, school, health cover and one car just to give you an idea.