Buttercream is a suitable filling or frosting for génoise as well as many other cakes.
There are three types of buttercream:
Classic buttercream (or pâte à bombe buttercream): Soft-ball sugar is poured into whipped egg yolks and then combined with a large quantity of unsalted butter.
Italian meringue buttercream: Soft-ball sugar is poured into whipped egg whites and the resulting meringue is combined with a large quantity of unsalted butter.
Crème mousseline: Pastry cream is beaten into a large quantity of unsalted butter.