I don't go off the beach much but I am aware that Floreat is not really great for launching due to the type of break (Dumpers) and that the council is not really keen on people going through swimmers on the off-weather sides of the groynes.
I am aware that there have been some issues with kiters doing the above recently from the Northern groyne (info from a 3rd party - I wasn't present).
If you are just wanting to blast out in the ocean (as opposed to wavesailing) you can pretty much launch anywhere.
I generally launch at Port Beach mainly as it is a relatively short walk to the water, you can rig on a concrete car park and there is likely to be a few others out, particularly guys on race gear to drag against.
The sailing is perfectly fine at City Beach / Floreat but the beach is massive so it's a long walk to the water.
On the plus side, you have nice lawn to rig on plus showers.
Brighton also offers a good combination of lawn, showers, other people sailing and a reasonable walk with your kit.
I spoke with the ranger who said they are fine with windsurfers as long as you don't launch between the groynes.
Other than the dumpers on your launch, it also seems to be more choppy off Floreat than it is further north or south.
I'd stick with Dutchies or Brighton.