The width of the table is almost equal to \textwidth. Why not go all the way and set it to \textwidth directly? Then, use a tabularx environment, allow automatic line breaking in the second column, and issue the instruction
\renewcommand\tabularxcolumn[1]{m{#1}}
to induce vertical centering in the non-X columns

\documentclass[12pt]{article}
%\usepackage[utf8]{inputenc} % that's the default nowadays
\usepackage[T1]{fontenc}
%%\usepackage[french]{babel}
%\usepackage{graphicx}
\usepackage[hmargin=1.27cm,top=0.7cm,bottom=1.3cm]{geometry}
%\usepackage{array,multirow,makecell}
%%%\usepackage{colortbl}
\usepackage[table]{xcolor}
%%%\usepackage{here}
%\newcolumntype{R}[1]{>{\raggedleft\arraybackslash}m{#1}}
%\newcolumntype{L}[1]{>{\raggedright\arraybackslash}m{#1}}
%\newcolumntype{C}[1]{>{\centering\arraybackslash}m{#1}}
\usepackage{tabularx}
\renewcommand\tabularxcolumn[1]{m{#1}} % vertical centering
\usepackage{fancyhdr}
\pagestyle{fancy}
% pour les pieds de page:
\cfoot{\scriptsize Trame du document : FOR\_TEMPLATE}
\rfoot{\scriptsize\color{red} Ne pas reproduire \slash\ Copie contrôlée}
\begin{document}
\begin{table}[!h]
\setlength\extrarowheight{2pt}
\begin{tabularx}{\textwidth}{|l|X|}
\hline
\rowcolor[RGB]{33,88,104}\multicolumn{2}{|c|}{%
\textbf{\color{white}Abbreviation}} \\ \hline
\textbf{Abbreviation} & \textbf{Meaning} \\ \hline
COO & Chief Operating Officer \\ \hline
RQ \& AR & Regulatory Affairs and Quality Manager \\ \hline
ANSM & Agence Nationale de Sécurité du Médicament et des produits de santé
(National drug and medical devices agency) \\ \hline
CPP & Comité de Protection des Personnes (Ethics Committee) \\ \hline
CNIL & Commission Nationale Informatique et Liberté
(French data protection agency) \\ \hline
CER & Clinical Evaluation Report \\ \hline
IFU & Instructions For Use \\ \hline
NC & Non-conformity \\ \hline
PMSR & Post-Market Surveillance Report \\ \hline
PSUR & Periodic Safety Update Report \\ \hline
CAPA & Corrective and Preventive Actions \\ \hline
\end{tabularx}
\end{table}
\end{document}
Addendum: While the preceding solution may satisfy the OP's direct requirements, I don't think it can be said that the table can be said to look attractive or interesting. If communicating effectively with your readers is something you value, you may want to give the table some stronger visual appeal by (a) removing all vertical and most horizontal lines and (b) simplifying the header material, along the lines pursued in the following solution. I hope you will agree with me that this table looks more inviting than the one shown above.

\documentclass[12pt]{article}
\usepackage[T1]{fontenc}
\usepackage[hmargin=1.27cm,top=0.7cm,bottom=1.3cm]{geometry}
\usepackage[table]{xcolor}
\usepackage{tabularx}
\newcolumntype{N}{>{\raggedright\arraybackslash}X}
\usepackage{booktabs} % for \addlinespace and \bottomrule macros
\newcommand\Tstrut{\rule{0pt}{2.6ex}} % 'top' (typographic) strut
\begin{document}
\begin{table}[!h]
\begin{tabularx}{\textwidth}{@{} l N @{}}
\rowcolor[RGB]{33,88,104}\multicolumn{2}{c}{%
\textbf{\color{white}Acronyms and their meanings\Tstrut}} \
COO & Chief Operating Officer\Tstrut \
RQ & AR & Regulatory Affairs and Quality Manager \
ANSM & Agence Nationale de Sécurité du Médicament et des produits
de santé (National drug and medical devices agency) \
\addlinespace
CPP & Comité de Protection des Personnes (Ethics Committee) \
CNIL & Commission Nationale Informatique et Liberté
(French data protection agency) \
CER & Clinical Evaluation Report \
IFU & Instructions For Use \
\addlinespace
NC & Non-conformity \
PMSR & Post-Market Surveillance Report \
PSUR & Periodic Safety Update Report \
CAPA & Corrective and Preventive Actions \
\bottomrule
\end{tabularx}
\end{table}
\end{document}
\newcolumntype{L}[1]{>{\raggedright\arraybackslash }b{#1}}to\newcolumntype{L}[1]{>{\raggedright\arraybackslash }m{#1}}(and possibly the same for the other column types), but is there a reason you had "b" there to begin with? – frabjous Jun 02 '22 at 14:33