I am French and I married a Brazilian. We live in Brazil and I go back and forth to France. I want to buy a property in France alone, can I do it without the intervention of my wife?

You married in Brazil and your first common home after your marriage was set in Brazil. You are therefore subject to the legal regime applicable in this country which is the separation of property. Therefore you can buy a property in France that will constitute a property. Your wife's intervention is not required.