Firstly it is a French study, so we can ignore it when we leave the EU? I found the takeaway quote "A lot of caution is being expressed about the study, but experts said a healthy diet is best." to be the most worrying. On the TV discussion they were advising not to change away from the established eating guidance, i.e. Eatwell. Whilst the Experts remain unchallenged, then any reseach is liable to be shot down in flames if it does not support the established regime.
Note: the study only established a weak correlation, which is not the same, or taken as implying, causation. Chicken / egg springs to mind. The only comment I have is that recent research is showing cancer needs glucose as fuel, and starving a cancer of this may lead to an eventual effective treatment, but it is early days. So there may be substance in their report after all.