Well, not so much an hard right, as some lip service to the right front in advance of upcoming elections, when talking about some topics that have been and will remain bothersome for the government in charge, whatever the brand, like how to deal with their immigrant population.
Macron is a centrist, an agnostic and a strong supporter since forever of the "laicité" of the state: this, and an emphasis on the assimilation in the "french" identity of immigrants have been an issue that have generated some internal conflicts even on the center-left of France parties when having to deal with the large muslim immigrant population, compounded with the residual issues from recent decolonization of largely muslim African French colonies, and have been doing so since forever.
He made some comments in this direction centered mostly on the laicitè stuff, but the big more generalized noises come from the old-guard of the France academia, like that article points out too.
The "old-guard" of academia, both left and right, is starting having to deal with the fallout of the attitude they took after the sexual liberation of the '60... it's likely that many, many members of the old guard have closets full of skeletons, by current standards (
https://www.theguardian.com/world/2021/feb/10/france-begins-to-confront-decades-of-neglect-of-incest-cases).
Let's say that having a guilty conscience about some past excesses is not exactly conductive to being open to a change of course that will lead to a reduction on your influence and prestige, and maybe even put your career in danger.