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Towels are provided for both on deck and in the cabin so you don't need to take them. Sorry cannot help on the straighteners or distance questions!!
You will be ok to use hair straighteners but the ship runs on 110 volts and you will need to take a plug converter suitable for the US (i.e 2 flat pins). You may also find they take longer than usual to warm up. Sorry but I can't help re Toulon but at least your hair should be nice when you visit St Trop!
Try the French Tourist board ( on line) for Toulon to St T.