How can I format an exercise between horizontal rules with a footer linking to the solution?

Here is an answer without TikZ: You must define the target label that the footer will link to with a command such as phantomsectionlabel{ans:imag} and then pass it to the environment as a parameter, such as begin{equation}{label:imag}. The phantomsection is not required if the target is a section, an environment created with newtheorem, or another command that is a valid link anchor in hyperref. If you get a warning about references that may have changed, recompile a second time and it will work properly.

I use unicode-math, but since you also specified PDFLaTeX: this approach would work just as well with classic packages. For example, all the symbols here are also in stix and stix2, or use your font packages of choice.

documentclass[12pt]{article}
usepackage[paperwidth=10cm]{geometry} % Solely to crop the MWE on TeX.SX.
usepackage[french]{babel}
usepackage{unicode-math} % Or your font packages of choice, e.g. bera.
usepackage{xparse} % For NewDocumentEnvironment
usepackage{xfrac} % For sfrac.
usepackage[svgnames, Svgnames]{xcolor}
usepackage[colorlinks, linkcolor=MediumVioletRed, unicode]{hyperref}

defaultfontfeatures{ Scale = MatchLowercase, Ligatures = TeX }
setmainfont{Fira Sans}[Scale = 1.0]
setsansfont{Fira Sans}
setmonofont{Fira Code}
setmathfont{Fira Math}
setmathfont[range={blacktriangledown, QED}]{XITS Math}

% Use the tombstone symbol for Q.E.D., as in some editions of DEK’s Art of
% Computer Programming.  Will be used at the end of exercises and also proofs.
DeclareRobustCommandqedsymbol{ensuremath{QED}}

% The imaginary unit, here set upright:
newcommandiu{symup{i}}

newcounter{ExerciseCtr}

NewDocumentEnvironment{exercise}
% It would be possible to specify formatting, such as "Exercise/Exercise"
% and the symbols in the footer, as parameters here, e.g. G{Exercise}.  In
% practice, YAGNI.
%
% The argument is the label of the answers, e.g. begin{exersise}{ans:imag}
{m}
{refstepcounter{ExerciseCtr}%
begingroupnormalfontbfseriesselectfont%
bigskipparnoindentphantomsection{}%
Exercice arabic{ExerciseCtr}endgroup*%
makebox[textwidth]{hrulefill}[0.5baselineskip]
begingroupnormalfontignorespaces%
}
{endgroup%
parnoindentbegingroupnormalfontttfamily%
hyperref[#1]{Correction (blacktriangledown)}%
hfillqedsymbolendgroup*%
makebox[textwidth]{hrulefill}%
medskipparignorespaces%
}

% Also provide an unnumbered exercise*, by analogy with the ams environments.
NewDocumentEnvironment{exercise*}
{m}
{%
begingroupnormalfontbfseriesselectfont%
bigskipparnoindentphantomsection{}%
Exerciceendgroup*%
makebox[textwidth]{hrulefill}[0.5baselineskip]
begingroupnormalfontignorespaces%
}
{endgroup%
parnoindentbegingroupnormalfontttfamily%
hyperref[#1]{Correction (blacktriangledown)}%
hfillqedsymbolendgroup*%
makebox[textwidth]{hrulefill}%
medskipparignorespaces%
}

begin{document}
noindent Lorem ipsum dolor sit amet.
begin{exercise}{ans:imag}label{exer:1}
Écrire sous la forme (a + iu b) les nombres complexes suivants:

  begin{enumerate}
    item Nombre de module (2) et d'argument
          (displaystylesfrac{uppi}{3}).
    item Nombre de module (2) et d'argument
          (displaystylesfrac{-uppi}{8}).
  end{enumerate}
end{exercise}

begin{exercise*}{ans:imag}
Un exercise.  
end{exercise*}

phantomsectionlabel{ans:imag}
Reportez-vous à l'exercice ref{exer:1}.
end{document}