Caravan Insurance - One for Paulette?

I am trying to get insurance for a caravan -- it's an ancient old thing, but we need to make it legal. We have car insurance with AXA through the agent in Gerardmer, so they seemed the obvious place to ask. However they wouldn't insure it, because they don't have our buildings and contents insurance? Which sounds odd to me, because having done some surfing around, it would seem that caravan insurance is normally part of your car insurance, not buildings and contents.

So is the agent trying it on in an attempt to get more business out of me (our B&C cover is with CA and is fine, and I have no desire to faff around more than I have to), or does this have some basis in fact? I am so miffed I'm tempted to cancel everything with AXA and start again somewhere else - we also have our mutuelle with them (renewal date beginning of April) .

At the moment the caravan is tucked away behind the garage, but we will need to move it in April because it becomes Tim's home during the summer, and goes to a campsite in Germany near the Luxembourg border. (Renting even the tiniest studio in Luxembourg is beyond our means!)

I may be wrong but was under the impression if you just need 3rd party cover on a towed caravan it is just added to your own car insurance and will be reflected in the document facts. Cover other than 3rd party needs a separate insurance if its over I believe 750kg. So as you mention it is "ancient" I assume 3rd party is all you want so in theory AXA should have no problem adding it to your car insurance. But hey this is France so who knows!