I too apologise for not always being prompt with my replies!
My husband was fluent in French when we moved here and I could get by - however, we found the Midi accent a culture shock since we spoke and understood 'Northern French'! I spoke/learnt French extensively throughout my schooling but had spoken it little since except on holiday - and I too found it was the confidence (to make mistakes with aplomb!) that I found difficult.
Having been very confident with his fluency when we arrived, if asked now my husband would say he was/is not fluent - but this is false modesty really given what he organised and the fact that all the locals always assume he is from Belgium (ie fluent in French but with a slightly odd accent)!!
My husband and the girls moved here in the April, whilst I continued to work my 6 months notice period in the UK (coming out here each weekend) until the August - so it fell to my husband to do all the organising.
We definitely dealt directly with each school and they made their own decisions - there was no interaction with the 'Local Authority'. Whether this is normal I do not know, it certainly was for us.
We did however visit the Mairie for our village to introduce ourselves as residents and this might have constituted 'contacting the Local Authority'?
Are you coming out in 2 weeks to then stay all summer? If so, I would consider popping in to the Lamalou school, explain that you are intending to move here for the September term and ask if your children could attend a few classes (maternelle probably) until the end of this term. The children would then get a chance to be at their 'new school' and you would be able to try out and see how you feel about it as well. At worst, the school can only say no - and even if they only offer one or more half days, it would help you and the children I think.
If you are staying the whole summer, why don't you book the children into the many summer organised events that are run - Lamalou has a lot going on.
When we first arrived here, we asked the girls if there was anything they had always wanted to do - and (after chosing a kitten each!) they asked to try horse riding. We let them do this just outside Lamalou for a few months as it helped introduce them to French people doing something special that they had chosen themselves.
The tourist Office has lots of info - it is worth a pop-in. ( http://www.ot-lamaloulesbains.fr/fr
) Some of the site is in English.
There is a different Headmaster now at the school and I will find out his name for you. I will also see if the English-speaking CP teacher is still there and send you the details.
I will send you my contact details. A good summer is on its way!!