a meaningful divide?

Le Monde published this map in its 26 July edition, to illustrate the contrast between South-East and North and West France(s). Meaning that the North-West upper part is more vaccinated than the South-East lower part of the map. The figure being computed as the sum of the differences between local and national rates, per age group, weighted by the group sizes. The paper goes on analysing the divide in terms of sociology of the territories, as well as political opposition to Président Macron… But I wonder (over breakfast) if it does not see too much in this picture. First some districts have to be either above or below the national average. Second, the map does not incorporate the population density: very sparsely populated districts in the South-East, like Auvergne or central Corsica are more visible than the densest areas like the Greater Paris, while being more prone to low vaccination rates due to the larger distance to vaccination centres. Third, most of the districts are within ±15% of the average, which may be too large for statistical variation but not much! The geographer Emmanuel Vigneron points out in the paper an inverse correlation between vaccination and earlier COVID cases, but this is not so surprising in that people who have already been exposed to the virus may conclude they are well (enough) protected. Further, the age effect is not eliminated by the contrast, in that areas with an older population are bound to get closer to the average, given that vaccination in the older groups started earlier and was more seen as a life-or-death issue. The soundest observation is rather in the opposition between urban districts where, despite an equivalent access to vaccination opportunities, the poorer burbs like the Northern districts of Marseille being the least vaccinated (with possibly an age effect?).