from a brief google search, it seems like you can make French buttercream with egg yolks or the whole egg.
i found a very nice page about buttercream on King Arthur Flour's website:
http://www.kingarthurflour.com/blog/2011/01/04/the-beautiful-side-of-baking-blissful-buttercream/
French: The method is the same as for Italian buttercream, but whole eggs or egg yolks are used instead of whites. VERY rich, and if youre not coloring the frosting, a very pale golden color. French buttercream has a lower melting point, because of the extra fat from the egg yolks.
French buttercream is the method. The whole egg method is not as popular as the yolk recipe. This is my frosting of choice at my bakery. It is very rich and accepts flavors, liqueurs, and fruits well. It's neighbor, IMBC, is not as rich and make a better blank canvas if richness is not the preference. So I use IMBC for more subtle frostings and FBC base for ones that need to be bolder.
French buttercream is the method. The whole egg method is not as popular as the yolk recipe. This is my frosting of choice at my bakery. It is very rich and accepts flavors, liqueurs, and fruits well. It's neighbor, IMBC, is not as rich and make a better blank canvas if richness is not the preference. So I use IMBC for more subtle frostings and FBC base for ones that need to be bolder.
good to know! makes total sense with how you put it. i've only tried making French once and i did like it. i'll try it more often with those suggestions 
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.
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I don't think they were making French buttercream or otherwise. They don't make that type of icing at Georgetown Cupcakes, and I don't know why they'd go to the expense of doing it on the burnt-to-cinders yet still raw "one ton cupcake".
I think they cut away to someone mixing batter, not making frosting.
I use a French BC everyday. It is great with vanilla, but as said above even better with flavor in it. I add preserves or liquers as well as other extracts. Crushed oreo's make it heavenly! To start the recipe I add 7 whole eggs to the stand mixer, with whip attachment on high, and whip the fool out of it until my sugar is cooked. It will make something that may look like a batter. All of the air bubbles in the eggs will insulate the raw eggs and keep them from turning to scrambled eggs when slowly adding the hot sugar syrup. If the eggs aren't very whipped, it will ruin. It's not hard at all, you just have to start them first, and by the time the sugar gets to "firm ball" your eggs will be ready. After sitting a couple of days at room temp, I sometimes have to re whip it but it never "breaks down" to me.
One note about FBC: It will deteriorate a little with over-mixing after the sugar stage. IMBC can be left alone and periodically checked for proper temp. But FBC will start looking like Play-Doh> It doesn't hurt the flavor, but it will noticeably decrease the volume.
This is my recipe. Use directions for IMBC. This recipe is always 1.5x by me for a 9 inch 3 layer cake.
6 lg egg yolks
1 c sugar
1/2 c water
2 c unsalted butter
Sugar to 238 degrees. When it is finished, 1 tsp of very hot or boiling water will make this recipe shine beautifully.
I use a similar recipe for one cake with the sugar slightly different, so a tiny adjustment is ok.
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