Disclaimer, I am not an expert, I just read too damned much once and I have forgotten a whole lot of it, LOL.

A couple things to consider:

Mountains indeed tend to occur at the edges of continents, but that is because these are near the edges of tectonic plates that are driving into each other. So it is not so much that continents have mountains on edges, as it is tectonic plates have mountains on their edges. If two equal sized land plates strike and form mountains, theoretically, you would have mountains in the middle of a land mass that people would call a continent. For instance, India is considered part of Asia, but is part of the Indo-Australian plate, which drives it into the Eurasian plate creating the Himalayas

Western coasts are cool water (relatively anyhow) while east coasts are warm water. If you think western Europe, consider the Gulf Stream's effects for warming that climate. Warm water and warm air bring more moisture than cold, which is important.

Wind direction and mountains are very important to precipitation. When air rises to travel over the mountain, it dumps water on that side, leaving what is called a rain shadow on the lee side of the mountain, and often dry warm winds. A quick quote:

On the lee side of the mountains, sometimes as little as 15 miles (25 km) away from high precipitation zones, annual precipitation can be as low as 8 inches.

So, no matter which way your winds are blowing, you have a river running between two ranges, so it is in a rain shadow from either direction. Possible? yes, but it needs explanation.

Forests: in a fantasy world in particular, it should also be noted that deforestation could easily be handled by extremely large herbivores running in herds, elephants, bison, buffalo and such can have serious deforestation effects, so, even larger critters could be real nasty on trees. I use this in one area of the Sister Continents. Fire can also be a major player in regions that are borderline forest worthy in precipitation or that experience regular droughts, such as the Great Plains in the US.