I had filet mignon once at a very classy Frech restaurant in Quebec City. It was served with a brandied mushroom sauce that was flamed at the table. My dessert was a creme puff shaped like a swan. I was only 14, and terribly impressed.
My mother and I loved fancy restaurants, and my father was happy to oblige, so we ate a lot of nice places. One place served new potatoes with their steaks that had been sauteed in butter until they were crusty brown on a couple of sides. I tried that at home, and they didn't get done, so they must have been pre-cooked a bit. I never did get around to perfecting that, but they were delicious with steak, and not too filling.
My husband used to take me to an old roadhouse that had been in business since the twenties. They made onion rings that I have since duplicated, and they are so easily done. They are sliced extremly thin...if you have a mandoline, it will make the job easier...then simply tossed in flour, and dumped by the handfull into hot grease. You don't have to deep fry them...a couple inches of oil in the skillet will do it. They fry up in no time, and all they need is a few minutes to drain and a sprinkling of salt. They are wonderful with steak.
I have never fixed filets at home...just nervous about ruining a beautiful piece of meat, I guess. But if I did, I'd serve them topped with the fried onion rings I described above, along with the butter sauteed new potatoes, and perhaps a small Ceasar salad.
I don't generally serve dessert unless we have company, but a dip of good French vanilla ice cream topped with a shot of creme de menth, Amaretto, or liqueur of your choice is always a good choice.