the colour fills the spaces surrounding the curve but the stroke line remains black.
This means that you are selecting the Fill color and not the Stroke Color. There are so many ways to assign colors in InDesign. Jane is showing you the two options on the Control panel, which I think is easiest for a new user, because there is a menu for Fill and one for Stroke.
If you opt to use the Swatches or Colors panel, pay close attention to the widget in the top left corner. There are two overlapping buttons, and one is always on top of the other. The one on top controls whether the color is assigned to the fill, or to the stroke.
Stroke on top vs Fill on top:
Thanks, this has solved the problem! I missed the fill/stroke toggle--it's well hidden.
Agreed! It is easy in the Control panel, not in the Swatches or Tools panel. By the way, "X" is the shortcut to toggle the Fill and Stroke as to which is in the front.
Be sure to mark one of these answers correct to close the thread, and I'm glad you are on your way!