Out of the blue my iPhone x fell out. I can't restart it. What can I do?

When you say "fell out", I'm guessing that the device has stopped, or are you referring to it falling out of a case, or what exactly do you mean? It may be a phrase that is something said in your local area, but it can mean different things here, since this is an international forum. But, I'll take a guess.

To perform a force restart on the iPhone X, follow the steps listed for the iPhone X in this support document. If your iPhone, iPad, or iPod touch won't turn on or is frozen - Apple Support

If your screen is black or frozen, you might need to force restart your device. A force restart won't erase the content on your device. You can force restart your device even if the screen is black or the buttons aren't responding. Follow these steps:

On an iPhone X, iPhone 8, or iPhone 8 Plus: Press and quickly release the Volume Up button. Press and quickly release the Volume Down button. Then, press and hold the Side button until you see the Apple logo.

At this point, you will need to make a Genius Bar appointment at your local Apple Store to have them take a look.

Ref: If your iPhone, iPad, or iPod Touch won't turn on - Apple Support