When I draw a rectangle shape in Photoshop it has colour properties.
But when I draw a line it has no colour properties and just uses currently selected colour.
I want to change the colours of lines I have already drawn. How do I do this?
You have two basic options: You can double click on the layer in Layer tab -> Layer style -> Color Overlay or
You can change the color if you select your shape layer and up there you will see the shape tollbar. Fill option sets the color of the shape.
Hope it helps.
On Any of the photoshop version, just press A on your keyboard, A bar will be displayed at the top, from there you can twist your shape to whatever you have including changing line color, increasing it thickness. etc.
As commented under question, pressing A solves the problem. The thing is, when you've selected a tool like Move tool (V), you're not in control of shape attributes, but you're more in control of object's positions and alignments.
When you select Direction Selection Tool or Path Selection Tool (A), it selects the part(s) of object and hence you get the options to alter them.