What is the correct mixing method for this kind of batter?
In France, that is a classic dessert called a Gâteau Fondant Aux Poires. In American English we'd call it a Pear Cake. Who can figure out the French and their dang desserts? What I can say, is that your instructions are fairly typical. In America we would call that a cake batter and wouldn't change a thing, except maybe to make it less fussy.