As they give you tracks and distances you fly the pattern using heading and stopwatch corrected for wind.
With all respect for all persons and opinions, I do not think this is common practice. Either you know the field, in which case you know the visual cues; or you don’t, in which case you will have little time or interest to fiddle about with a stopwatch, let alone wind corrections. You will be more than busy with the radio, looking out for other traffic, finding the visual references, all while not forgetting to fly the aircraft.
A circling is a visual manoeuver under bad weather conditions, otherwise you could fly a normal visual pattern.
I may have the context wrong, but I would have thought that a “circling approach” is simply what you do if there is no IAP for the current runway.
Normally the desired track is just “common sense” (a break to the right, onto downwind, and flying a proper tight left base to the runway) but in this case the desired track is published for some reason which can be obstacles or noise abatement.
I am not sure there is a necessary “bad weather” angle. A jet is not likely to fly VFR into LFAT and hope that they haven’t cleared somebody in French for the same runway (as has happened to me twice so far – a head-on near-miss on base leg!). They will fly the ILS and go straight in, or fly the ILS and circle to land.
Many airlines around the world ban circling approaches totally because the pilot needs to be able to actually fly a plane 
That view is correct. This is not a circling approach but a specific procedure. If you are IFR and need to land on RWY31 you will be given the VPT, but you do not need necessarily to descend to MDA. The visual circuit is to the north of the RWY.
I don’t rely on ground points because the VPT may be flown in poor viz, down to 1500m in CAT A. In the unlikely event that you ever flew it down to that viz you probably would not have the field in sight until short final.
In practice its no problem. At 120kts turn right onto 180deg for 1min then left onto downwind for 90secs, rate one turn onto final.
that a “circling approach” is simply what you do if there is no IAP for the current runway
that is correct, but nobody would fly this procedure at 600ft when the weather is fine. You fly it after an instrument approach when the tailwind prohibits a landing on RWY13 and additionally you could have a low ceiling. If you have no clouds, fly it at a higher altitude – the final is long enough.
If you fly this procedure you know the highest obstacle in the area will reach up to 263’ (trees)
In the unlikely event that you ever flew it down to that viz you probably would not have the field in sight until short final.
If you loose visual contact with the runway for more than a few seconds you shall fly a go-around.
Are you sure that you need to have visual contact with the RWY throughout a VPT procedure? I had understood that clear of cloud and in sight of the surface was the requirement. Do you have a reference for this?
BTW the SIA defines a VPT as “Visual manœuvring using prescribed track”.
e.g. FAR § 91.175 (e) (2)
(e) Missed approach procedures
Each pilot operating an aircraft, except a military aircraft of the United States, shall immediately execute an appropriate missed approach procedure when either of the following conditions exist:
(1) …
(2) Whenever an identifiable part of the airport is not distinctly visible to the pilot during a circling maneuver at or above MDA, unless the inability to see an identifiable part of the airport results only from a normal bank of the aircraft during the circling approach.
@ Ted.P here they don’t call it runway but identifiable part of the airport – so it can also be the well illuminated terminal building 
Now you can argue that VPT is not a circling. But I must say indeed it is a circling manoeuvre with required MDA and visibility – French extravagancy with prescribed tracks.
There are two sorts of visual manoeuvring:
VM(C) (visual manoeuvring circling) where obstacle clearance is guaranteed within a particular distance of the thresholds
and
VPT (visual manoeuvring on prescribed track) where obstacle clearance is guaranteed within a particular distance of the prescribed track
France seems to like VPT, and most other states don’t use it.
You can carry out a circling manoeuvre without seeing the runway if you have other (prescribed) visual references. E.g. see this procedure: https://www.ippc.no/norway_aip/current/aip/ad/enra/EN_AD_2_ENRA_5-1_en.pdf . I haven’t flow it for real, but I have in a full visual simulator. Interesting, to say the least.
The puzzling thing about this VPT approach is why it exists. There does not seem to be anything to prevent an NDB IAP to RWY31. It would be a lot more comfortable to remain at 2000’ and then do a timed (or DME) base turn, like the existing NDB IAP to RWY13.
As it is the VPT flown at minima is often very rough with turbulence and the locals probably don’t appreciate aircraft being flown very low over the town in approach config at high power. VPTs make sense at locations such as Cannes and Nice due to terrain. But why Le Touquet?
I dont see why this circling pattern should present a problem in most GA types at 600 feet? There are plenty of visual clues that correspond with the “plate” and the pattern is actually pretty generous to allow for gentle turns. I seem to recall the missed with circle to land just down the road at Calais is similiar and didnt present any issue in the Aztec recently.
