The notaire is the legal link between 2 parties, in the case of property purchase, this would be the buyer and the seller of the property. It is their job, among other things, to make sure that the property has no debts outstanding, or claims made upon it. They will prepare all the legal paperwork for both parties & collect any taxes due to be paid on the purchase or sale. Their fees for this service are fixed by the French Government, and are around 6% to 8% depending on the value of the property;  the fee charged will be the same from every notaire. 
When you decide to buy a property in France, you & the seller will be required to sign a document called the compromise de vent  (the joint promise of sale) & to submit a deposit of 10% to the notaire. The notaire will then start to complete the rest of the legal paperwork which can take between 6-8 weeks. When all these documents have been finalised, you can return to the notaire to sign the final documents, pay the outstanding balance, the notaires fees & collect the key!