Mike, 

if there is something unusual about the English that may apply in America, it applies in Australia too. The verb-verb construct ‘ going  (to) do ‘ is not the same as that used in the example , which is verb-noun,  ‘ going for a walk ‘.

‘ (to be) Going for a walk..’ can definitely mean ‘currently walking’ or ‘about to go for a walk ..’ in everyday Australian English usage. I don’t think it necessarily implies the necessity of any other form of transport being used to get the walk underway, although in specific contexts it might.

Partly this overlap in English meaning arises because we can and often do say ‘ going walking ..’ instead of ‘ going to go walking…). 

In French, present tense is also used where in English we would use present simple or present continuous, and can also be used for near future. 

The important point of the lesson and the example is the French distinction between using ‘se promener’ - taking themselves for a walk with the dog tagging along - as opposed to ‘ promener’, which would indicate the purpose was to walk the dog.

Expressing immediate and near-future actions with the present tense (Le Présent) in French 

Expressing "to walk" with se promener/promener/marcher/aller à pied in French