European beech is closely related, but if I read the data correctly, it is a rather tension-weak wood.
I know the data in the wood database are rather conservative, but they seem conservative in a consistent way, so you can tell relative to a known species how good a wood is as a bow wood.
http://www.wood-database.com/lumber-identification/hardwoods/american-beech/http://www.wood-database.com/lumber-identification/hardwoods/european-beech/Using red oak as a reference of medium-quality bow wood (we all have made bows out of it), American beech is a bit better, allowing back fibers to be stretched a bit more (this is given by MOR/MOE; the resulting number is the percentage the back can safely stretch before breaking). It is also about 10% better in compression than red oak (this is given by crushing strength/MOE; so it will take less set for the same design). It has about the same density, and the same stiffness (MOE) as red oak. So overall, in a same design as red oak, it can be drawn further and can therefore store more energy before taking set or breaking. Alternatively, one could make American beech bow limbs a tad thicker, increasing draw weight for the same draw length.
American beech is more on less on par with European ash, which is commonly considered a rather decent European bow wood.
European beech, however, is slightly weaker in tension than red oak (the back wood cannot stretch as far; it is one of the worst European hardwood species in tension), and similar in compression strength. It is about 12% stiffer than red oak (a bow that is 12% narrower than a same design read oak bow will have the same draw weight). So if you want to make European beech bows, make them a bit longer than you would do with red oak.
Now, I bet that where you live there is also plenty of European maple or norway maple. Both are very good bow woods, despite having lower density. I'd make them 20% wider than your typical red oak bow, but you can make them a bit shorter too because of their higher maximum tension and compression load before break/set.
Joachim