Leave off the word "French" and you'll find all sorts of recipes for buttercream icing. Here are a few:

Here is a link that might be useful: Buttercream Icing

Google French buttercream and you will find lots of recipes....some using egg whites, beaten to lighten the frosting and others using folded in whipped cream and still others using a cooked custard with milk, eggs and flour as a base and adding butter and sugar to that. I like one with whole eggs like the link below.
Linda C

Here is a link that might be useful: french buttercream

Thank you! Plan to try a few this weekend. Will let you know if it worked out.
Kim

The trick with smooth butter cream is to beat it for a long time. Here's one of my favorite. It is so smooth and velvety it almost melts in your mouth.

BUTTERCREAM FROSTING

Cream l/2 cup butter with l/2 cup shortening
Cream till very soft. Slowly add 1 cup granulated sugar and beat 10 minutes.
Heat a small can of evaporated milk (one of those tiny 5 l/2 oz. cans) till luke warm (not hot) and slowly beat into sugar and butter mixture. Add 1 tsp. vanilla and beat for 5 more minutes.

One amazing way to use this recipe is to frost a devilsfood chocolate cake with it, chill it in the fridge or freezer, and top it with this wonderful chocolate frosting (chocolate devilsfood butter cream cake).

Here's the chocolate frosting:

In top of double boiler melt 3/4 cup shortening and 3 double squares of baking chocolate (6 oz). Keep this warm. Meanwhile, heat l/4 cup plus 1 Tbsp. milk. Add the hot milk to one box of powdered sugar, along with one tsp. vanilla. (I beat it in a stand mixer) When milk/sugar mixture is smooth, add warm chocolate/shortening mixture. Beat only until it is thoroughly mixed so it doesn't cool too much. Pour this over the chilled buttercream frosted cake. If you grew up in Detroit, this cake is a lot like (only better than) Saunder's devilsfod buttercream cake.