American oak and French oak are the same species of tree, just planted in different areas.
There are approximately 300 species of oak that grow around the world. Three main types are used in winemaking. They are the American oak Quercus alba (mainly from the Midwest) and the French oaks Quercus robur and Quercus sessiliflora (aka Quercus petraea.) While most French oak is from France, the two species of oak grown in France also grow in Austria, Hungary, and other parts of eastern Europe. Highly sought-after oak barrels are now made with wood from those countries as well. The flavor American oak imparts to wine is different from the flavor French oak imparts. American oak is heavier, denser, and less porous than French oak. It tends to be less tannic and have more pronounced vanilla and sometimes coconut-like flavors. French oak is more subtle in terms of flavor, somewhat more tannic, and allows for slightly greater—but still limited—ingress of oxygen. Neither type of oak is necessarily better than the other, in the same way that basil isn’t necessarily better than rosemary.