problems with landlord

I have a problem with my former landlord. Here are the facts:

I signed a contract (bail) which started 15 july 2005. I pay rent (around 2000 € pr month) in advance.
I canceled the contract according to article 16 with 3 months "preavis" to the 1st in a month (letter dated 27 september, end of contract 31 december)
The 27/11 the landlord calls Etat de lieu on my behalf for the 18/12.
I paid last rent 15 december - (one month - in my oppinoin ½ month as rent to 1 january and ½ mont as part of payment of the etat de lieu-bill).
Etat de lieu said on the 18 december that we shall pay around 7.200 € (3.200 for painting, gardening and so on plus 4.000 € as 2 months rent). We accepted the amount.
The 21/12 we hand in the last key to landlord.

I paid 7.200 € (the 1.000 € paid in advance, 6.000 € transfered from the blocked garantie bancaire, and 200 € by virement).

I have documentation of all these things.

The landlord's lawyer tells me that I have to pay rent to 15 january - ½ month extra. In the contract is written that "le loyer annuel est fixe á la somme de 24000 € soit 2000 € par mois ... par anticipation ... pour le 15 de chaque mois." In other words: The contract doesn't mention half months rent, so I have to pay a whole month rent on the 15 december regardles that the contract terminates the 1 january!

Can that be correct??!