In English one who engages in the common act of strolling is peripatetic, and is referred to in the same manner. A peripatetic. Any difference between the adjective and the replacement noun have little meaning in common usage.
The French actually have a word for this peripatetic culture. Flâneur. Generally translated it is noun for “an observant stroller”. However, Charles Baudelaire a 19th century poet offered a much more empathic vision for the role of the French Flaneur when he wrote in a very lengthy essay.
“The crowd is his element, as the air is that of birds and water of fishes. His passion and his profession are to become one flesh with the crowd. For the perfect flâneur, for the passionate spectator, it is an immense joy to set up house in the heart of the multitude, amid the ebb and flow of movement, in the midst of the fugitive and the infinite. To be away from home and yet to feel oneself everywhere at home; to see the world, to be at the centre of the world, and yet to remain hidden from the world – impartial natures which the tongue can but clumsily define. The spectator is a prince who everywhere rejoices in his incognito. Thus the lover of universal life enters into the crowd as though it were an immense reservoir of electrical energy. Or we might liken him to a mirror as vast as the crowd itself; or to a kaleidoscope gifted with consciousness, responding to each one of its movements and reproducing the multiplicity of life and the flickering grace of all the elements of life.”
Charles Baudelaire, “The Painter of Modern Life”, (New York: Da Capo Press, 1964)