I am buying a property which is worth 15,000 euros. The signing of the final agreement takes place next week. I sent a check to the notary corresponding to the sale price and the purchase costs, but they told me that I have to make a bank transfer (...)

... Is that right?  

Yes. When the notary receives or makes a payment on behalf of the parties for a deed that it draws up in the authentic form and publishes in the real estate file, this payment must be made via a transfer (art. L.112-6-1 Monetary and Financial Code), unless the amount is less than 3000 euros (art. R.112-5, I CMF).