Marcel Pérès has claimed that, by the time of Gajard, much of the chant at Solesmes was sung as much as a fifth higher than what had previously been customary in France. You might take a look at @Charles_Weaver's post about church keys—and keep in mind that the old tuning standard in France was a whole step lower than modern concert pitch! There is just no way to take head voice down that low. The "Frenchified" (as one of my priests used to call it) sound isn't unique to the Solesmes congregation; in my experience, it's fairly widespread among TLM communities. I have no proclivity toward it at all and would prefer for my men to sing like Romans, not Frenchmen. Another component of that French style seems to be encouraging singing with a constantly raised soft palate. I would be interested to hear what others have to say about this specifically.

As for light consonants, are you hearing something that is quantitatively different, i.e., simply weaker consonants, or a qualitative difference, i.e. dental ts and unaspirated consonants? Very often, it is possible to detect Anglo/American choirs in otherwise very fine recordings in Italianate Church Latin simply by how hard they attack plosive consonants. It's not the Roman style. Neither is singing Latin with a French accent!