Here are some examples:
Take this example, from Corrine Jackson:
I hope you putrefy in hell, you prevaricating cheat. I'm glad to be emancipated from you!
I hope you rot in hell, you lying cheat. I'm glad to be free from you!
The "French" sentence is wordier, slightly more flowery, and gives off an air of intelligence. It is also less direct. The "Germanic" sentence, which uses shorter words, is sharper and to the point.
Another noticeable difference concerns the food-based vocabulary. Cows were what the Anglo-Saxon peasantry farmed, beef was what the Norman aristocracy ate.
Of course, this doesn't always work. In the pairs weep (Germanic origins) and cry (French origins), for example, the Germanic word seems to be of a slightly higher register than the French word. Nevertheless, as a rule of thumb, it's a good one.