French Buttercream can be made using egg yolks only, egg yolks and whole eggs, or just whole eggs.
To make the buttercream,
1. Yolks only: make a Pâte á bombe - boiled sugar syrup poured over whipped egg yolks. Butter is then beaten into the cooled mixture.
2. When using egg yolks/whole eggs, or just the whole eggs, use either the boiled syrup [Italian meringue method] or beaten over simmering water [swiss meringue method] ..
It is softer and richer than the buttercreams made using egg-white meringue. It is also yellow as it includes yolks. It breaks down quicker even though it is a cooked frosting due to the presence of the yolks.
Flour Frosting [faux "whipped" cream frosting] is sometimes called French Buttercream.