Assuming he also has the grade of professeur, that might be something like:
M. Emmanuel Trudeau, Professeur, HDR, Université de Paris I
Otherwise, that might be:
M. Emmanuel Trudeau, Maître de conférence, HDR, Université de Paris I
M. Emmanuel Trudeau, Docteur en 'Pataphysique, HDR, Université de Paris I
The capitalization of the first noun is not mandatory. It is capitalized when using the traditional conventions but publishers can choose to use simplified ones where only the first word is required to be capitalized (here Le).
Note that this non capitalization can be found elsewhere, for example in this book:
Sometimes the rules are broken and fully ...
As far as I know, the HDR is an additionnal degree in French universities that allows a researcher to evaluate thesis and to be candidate to become a professor. He must therefore have a PhD (or equivalent) but he does not have the grade of Professor. Therefore I would suggest :
Dr. Emmanuel Trudeau
Indeed, this would be consistent with the other ...
A complementary answer based on my experience.
In fact, I have posted a relevant question
Translate academic titles (lecturer, assistant and associate professor, tenure track, instructor)
for academic titles. Based on the comment feedback I consulted academia.stackexchange.com