I have observed many times whenever there is rise in the price it will proportionally increase the fees as well.
The price rises as more people use Bitcoin. The fees rise as more people use Bitcoin. The price does not cause the fees to rise, but they are related, as you can see.
Also, sometimes when there is a quick rise in price, people flood the block chain with transactions, presumably moving coins in and out of exchanges. This causes the fees to rise temporarily.