I believe that this map actually exactly shows, at the contrary, that the french are not more genetically different to other latin countries. 
- We just have to look at the distance between the “average situation” of Spain to notice that the distance it separates to Italian “average situation” is actually much farther than the distance with the “average french position”.
- The map actually show us a bigger overlap between the french samples (taken in Lyon) and the Spanish/Catalan samples (taken in Barcelona), than between them and Italian samples taken in Rome.  Globally speaking the overlap between Spain and Italy is very limited, most of Italian cluster is globally much distant.  We can easily image that if the french samples were taken in areas of the south, south-west of the west, those would probably be even closer than they are with samples taken in Lyon.
- Bourgogne and Lyon is usually said to be relatively more “nordic” than a big part of the rest of France, especially the regions of the south and the west (the north-east and north would be a little bit closer to the south German or Austrian cluster).  If we had samples taken in Bordeaux, Toulouse, La Rochelle, Poitiers, etc…  it is higly probable that the results for France would be even closer to Spanish samples, especially if those samples would be taken in Cataluna, Aragon or Pais Vasco.
- You said that the map showed that the french were basically a mix of Germanic and Celtic people…  Well I don’t know where on the map the ”celtic” cluster you speak about is supposed to be?  What area is the references of ”celticness”. 
Is it Ireland? What the map tell us is that the Irish are not genetically different to the other British (English sample taken in Kent in south-east England); but also largely overplap with Netherlands or Norway…  If the Irish are supposed to be reference of what is supposed to be a “celtic” ethnicity, and we french would have a majority of “celtic” compoanant as you said, we would see it on the map… Actually we see the reverse, French and Irish samples are completly non-overlaping.
Since the origin of Germanic cultures is historically around Denmark, and if we suppose that there is such a thing as a “germanic” ethnicity, this ethinicty should be more or less centred around the clusters of Denmark (where largely overlap the samples of Northern Germany, Netherlands, Norway, and England).   If, as you said, french people were a genetic mix of those people with the “celtic” people of Irish type,  our position on the map should be overlapping on England sample…  Which is not the case at all.
Or maybe you consider the term “celtic” in the more historical point of view, considereing that the point of origin of celtic people is the area around southern Germany and Austria. (and then have to accept that Irish people are not at all ethnically “celtic”, contrary to the common thought spread by Irish nationalism since the 19th century to try to take distance with the English, but are basically ethnically “germanic”.)
So, if the ”genetic celts” are basically the population of Central Europe (Samples of southern Germany and Austria);  the “genetic Germanic” are from the population of denmark/northern Germany/Norway and if we french people are supposed to be a mix of those “celts” and those “Germanics”, as is usually said by many people (as you said), we would have found the french samples on the map centred about the areas of Southern Germany and Northern Germany!   It is absolutly not what we observe on the map!  On the contrary, the french sample center below the supposed “celtic” cluster of  Southern-germany and Austria…  Since on the map it is situated between southern Germany and Spain (Cataluna).  The map learns us that the french cluster is situated at exact distance between the central Spain cluster (Madrid/Castilla) and the “Germanic” cluster – How could we say that the french are basically a mix of Germanics and Celtic ethnicities??  since, in all definitions of these groups, these groups are situated “more to the north than the french cluster is.  If you consider the Central Spanish cluster as a “latin” or “mediterranean” cluster, then you should conclude that the french can’t be basically a mix of “Celtic” and “Germanic” people, but should be at least 50% Spanish/mediterranean, and maybe 25% Celtic and 25% “Germanic”.