How to remove headrule in chapter page without remove of footrule, eg, rule only in foot page in all pages, but without on chapter page, but headrule in others pages.
\documentclass[a4paper]{memoir}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\copypagestyle{rgstyle}{headings}
\makeoddhead{rgstyle}{}{}{\slshape\rightmark}
\makeevenhead{rgstyle}{\slshape\leftmark}{}{}
\makeoddfoot{rgstyle}{R\'egis $\smiley$ \the\year}{}{\thepage}
\makeevenfoot{rgstyle}{\thepage}{}{R\'egis $\smiley$ \the\year}
% add line
\makeheadrule{headings}{\textwidth}{\normalrulethickness}
\makefootrule{headings}{\textwidth}{\normalrulethickness}{\footruleskip}
% fix plain
\copypagestyle{plain}{rgstyle} % overwrite plain with rgstyle
\makeoddhead{plain}{}{}{} % remove right header
\makeevenhead{plain}{}{}{} % remove left header
\pagestyle{rgstyle}
\begin{document}
\chapter{Memoir without headrule in chapter page}
\lipsum
\end{document}

