If a president hasn't been chosen, you can just for the moment use the \examiner macro instead of the \committeepresident one.
The design of the title page is indeed sadly hard coded (plans to change this but no before few months) so the best way to achieve your need is to redefine some part of it, here the (private) macro \YAD@committee@tabular which defines a tabular, the specification of which (that is by default >{\itshape}llp{5cm}l) being easily changed.
Here is a MWE:
\documentclass[mainlanguage=english]{yathesis}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
%
% Modification of the committee tabular
\makeatletter
\renewcommand*{\YAD@committee@tabular}{%
\small%
\begin{tabular}[t]{>{\itshape}llp{8cm}l}
\multicolumn{4}{@{}l}{\bfseries\YAD@translation{committeemembers}}%
\\[.25cm]
\DTLforeach*{YAD@staffs}{%
\YAD@the@staff=YAD@the@staff%
}{%
%
\YAD@display@staff{\YAD@the@staff}%
}%
\end{tabular}%
}%
\makeatother
%
\supervisor[professor,affiliation=ULCO]{Michel}{de Montaigne}
\cosupervisor[associateprofessor*,affiliation=ULCO]{Charles}{Baudelaire}
\comonitor[associateprofessor,affiliation=ULCO]{Étienne}{de la Boétie}
\referee[professor,affiliation=IHP]{René}{Descartes}
\referee[seniorresearcher,affiliation=CNRS]{Denis}{Diderot}
% Currently, we're not sure Victor Hugo will be the committe president...
% \committeepresident[professor,affiliation=ENS Lyon]{Victor}{Hugo}
% ... but we know he will be an examiner
\examiner[professor,affiliation=ENS Lyon]{Victor}{Hugo}
\examiner[associateprofessor,affiliation=Université de Paris~13]{Sophie}{Germain}
\examiner[juniorresearcher,affiliation=INRIA]{Joseph}{Fourier}
\examiner[juniorresearcher*,affiliation=CNRS]{Paul}{Verlaine}
\guest{George}{Sand}
%
\begin{document}
\maketitle
\end{document}

\documentclassand ending with\end{document}. – Bobyandbob Dec 03 '17 at 18:25\begin{minipage}[c][\YAD@otherboxheight][c]{\YAD@titleboxwidth}by\begin{minipage}[c][\YAD@otherboxheight][c]{\textwidth-2\fboxsep-2\fboxrule}(about line 2680 in yathesis.cls) – pluton Dec 03 '17 at 18:57etoolboxpackage – pluton Dec 03 '17 at 19:03\textwidth-2\fboxsep-2\fboxrulebut got an undefined control sequence and an illegal unit of measure error. Also how should I use the etoolbox. I tried to play with that parameter but nothing changed – user3371583 Dec 03 '17 at 19:11\textwidth\fboxsep\fboxruleare well defined I believe. – pluton Dec 03 '17 at 19:44\fboxsepis undefined. I tried playing with that parameter a bit but it didn't change the size of my table sadly. – user3371583 Dec 03 '17 at 20:15