When you say no grains, do you mean just grains and grain-like foods that contain gluten, or no grains at all? If no grains at all, that means you've eliminated complex carbs, which supply a lot of our energy. Every civilization has eaten grains or grain-like fruits such as quinoa and buckwheat as their staple food for eons, so that could explain it. For most people, the problem isn't gluten, it's wheat, though some people do have a gluten problem, but there are tons of grains and grain-like fruits out there that don't contain gluten, such as brown rice, teff, amaranth, quinoa, buckwheat, millet -- there's a lot out there. It could also just be a period of adjustment, as often happens when dietary changes are made, and you've made a big one, that time will fix.
That's not necessarily true anymore -- world trade pressure affects Europe, too, and some of the largest GMO companies are in Europe. In the US, you can find non-GMO foods easily at any health food store, and even in the grocery store. Just look for organic. To be certified organic, it means none of the harshest pesticides, no GMOs, etc. And while it's true grains aren't like they were then they were wild, people stopped eating wild grains when agriculture was established, and that was a very long time ago. You just have to work at it harder, and you would have to work at it in Europe as well. Remember, most of the organically grown food in the world is grown in the US.