Looking at that map of sites in France alone, randomly distributed is a good first approximation for figuring out the probability.
Pondered the estimation a bit more. The first two points of a group of 7 define a line. The probability of the remaining five being close enough to the line is just the probability of each being close enough, to the power of five. We can roughly estimate that probability as the "close enough" distance divided by the total area. Let's just normalize. Let's assume distribution within a unit square Some of the lines would not cut in a way that most of the "close enough" area is inside the box, but that's a constant factor and not to big.
Given n points and the probability p7 that seven points lie close enough to a line, we take the number of different sets of seven points, N7 = (n choose 7). The likelihood of a match is (1-(1-p7)^N7).
This is a very rough estimation, of course, but it gives some idea of the likelihood.
