After many search, I have found how to have a pretty good UTF8 mapping (which give no bad result on Acrobat Pro accessibility checking) for lmodern and amsfonts.
The code needed is in the minimal example below (Maybe some of you maybe interested so I commented it a little).
But now, I decided to change my font to the one of the fourier package and I have some difficulties to figure how to get proper UTF8 encoding in the output pdf with this font.
Normally I should add commands like the following:
\pdfglyphtounicode{<IdentifierSymbol>}{<UTF8Code>}
But I don't know where to find what I have called call the <IdentifierSymbol> and <UTF8Code>. I have done many test but without success.
I would greatly appreciate your help.
Here is the minimal example to show the difference of UTF8 mapping when using Fourier fonts instead of Latin Modern font. You can see the difference by copy-pasting the content or by an accessibility check if you have Acrobat Pro.
\documentclass[]{article}
%PdfTeX settings for a correct UTF 8 Mapping
%------------------------------------------------------
\usepackage{ifpdf}
\ifpdf \input{glyphtounicode.tex} %Part of modern distribution
%%%\input{glyphtounicode-cmr.tex} %Additionnal glyph: You must grab it from pdfx package
\pdfgentounicode=1
\else %Place here the settings for other compilator
\fi
%Encoding + cmap (to get proper UTF8 mapping)
%------------------------------------------------------
\usepackage{cmap}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
%NB: CHANGE lmodern AND fourier TO SEE THE PROBLEM OF MISSING UNICODE CHARACTERS
% You can see this on Acrobat Pro with acessibility checking or simply by copy-pasting the content.
% Of course copy paste is not perfect in both case but it is better with lmodern
%------------------------------------------------------
\usepackage{lmodern}
\usepackage{fourier}
%AMS Math + UTF8 mapping of ams symbols
%------------------------------------------------------
\usepackage{amsmath}
\usepackage{amssymb} % I load it after Fourier else I have more incorrect utf8 mapping (with \geqslant for example)
%Correct UTF8 mapping for ams fonts
\ifdefined\pdffontattr% \ifdefined is part of the e-TeX extension, which is part of any modern LaTeX compiler.
\immediate\pdfobj stream file {umsa.cmap}
{\usefont{U}{msa}{m}{n}\pdffontattr\font{/ToUnicode \the\pdflastobj\space 0 R}}
\immediate\pdfobj stream file {umsb.cmap}
{\usefont{U}{msb}{m}{n}\pdffontattr\font{/ToUnicode \the\pdflastobj\space 0 R}}
\fi
%Start document
%------------------------------------------------------
\begin{document}
Issue with mapsto : ${\mathcal F} : \boldsymbol{\eta} \in {\mathbb{R}}^{np}\ \mapsto {\mathcal F}\left(\boldsymbol{\eta} \right)\in \mathbb{R}$
\bigskip
Issue with sqrt : $\sqrt{X}$
\bigskip
Issue with parenthesis : $X \geqslant \left(\frac{1}{2}\right)^2$
\bigskip
Issue with sum : $\sum_{n=0}^\infty X^n$
\end{document}