https://tex.stackexchange.com/q/428330/35864

xawi-theses.tex

\documentclass{article}

\usepackage[utf8]{inputenc}
\usepackage[french]{babel}
\usepackage[style=authoryear]{biblatex}

\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@phdthesis{normalthesis,
  author = {Author Normal},
  title = {Title PhD Thesis},
  date = {2016},
}
@thesis{mormalthesis,
  author = {Author Mormal},
  title = {Title PhD Thesis},
  date = {2017},
  type = {phdthesis},
}
@thesis{mythesis,
  author = {Author These},
  title = {Title Thèse},
  date = {2014},
}
@habilthesis{habilthesis,
  author = {Author Habilitation},
  title = {Title Thése Habilitation},
  date = {2014},
}
@thesis{habilthesis2,
  author = {Author Habilitation},
  title = {Title Thése Habilitation},
  date = {2014},
  type = {habilthesis},
}
\end{filecontents}

\addbibresource{\jobname.bib}

\NewBibliographyString{thesis,habilthesis}

\DefineBibliographyStrings{french}{
  thesis = {Thèse},
  habilthesis = {Thèse d'habilitation},
}

\DeclareStyleSourcemap{
  \maps{
    \map{
      \step[typesource=habilthesis, typetarget=thesis, final]
      \step[fieldset=type,          fieldvalue=habilthesis]
    }
    \map{
      \pertype{thesis}
      \step[fieldset=type, fieldvalue=thesis]
    }
  }
}

\begin{document}
\nocite{*}

\printbibliography

\end{document}