Open Steam Big Picture mode with the icon next to minimize

Depending on your controller, you may have to enable configuration by navigating to settings


Then select Controller Settings


Check the box to enable configuration for your controller

Open your library

Select Dark Souls Remastered, then Manage Game, then Controller Configuration

Navigate to the Left Stick and select it

From here select Additional Settings

In the Additional Settings menu select Output Anti Deadzone

Move the slider to the right to adjust the yellow circle's size. You may need more or less than is shown in this image

After that you may find it difficult to input a slow walk. To fix this, select Anti Deadzone Buffer under the previous Additional Settings menu.

Adjust the slider to show a smaller dark circle within the yellow circle. By adjusting these two settings you should be able to run consistently.