This question was already raised and answered here for american:
\documentclass{article}
\usepackage{csquotes}
\usepackage[american]{babel}
\DeclareQuoteStyle[american]{english}% verified
{\textquotedblleft}
[\textquotedblleft]
{\textquotedblright}
[0.05em]
{\textquoteleft}
{\textquoteright}
\MakeOuterQuote{"}
\begin{document}
"This is a quotation," he said. "It continues onto the next paragraph.
Here is the continuation of my quote. As per literary convention,
there is no end-quote at the end of the previous paragraph."
\end{document}
But I need to adapt it for french.
Normally, in a LyX document, putting the first part before \begin{document} in the preambule, and the rest except \begin and \end in the LyX editor should work (except document class is declared in the LyX interface, and LyX declares \language).
First problem: in the pdf produced, I don't have the middle quote (the one which begins the intermediate paragraphs.
Second problem: I have tried to adapt the code for french, but without success:
%\documentclass{article}
\usepackage{csquotes}
\usepackage[frenchle]{babel}
%\usepackage[american]{babel}
\DeclareQuoteStyle[french]{guillemets}
%\DeclareQuoteStyle[american]{english}% verified
{\guillemotleft}
[\guillemotleft]
{\guillemotright}
[0.05em]
{\guillemotleft}
{\guillemotright}
\MakeOuterQuote{"}
The pdf output is exactly the same. But I assume it is linked to point 1. So, here is the full LyX code (\language shall be edited by hand in a text editor, otherwise, LyX proposes français in its interface, but then it issues an error):
#LyX 2.1 created this file. For more info see http://www.lyx.org/
\lyxformat 474
\begin_document
\begin_header
\textclass article
\begin_preamble
%\documentclass{article}
\usepackage{csquotes}
\usepackage[frenchle]{babel}
%\usepackage[american]{babel}
\DeclareQuoteStyle[french]{guillemets}
%\DeclareQuoteStyle[american]{english}% verified
{\guillemotleft}
[\guillemotleft]
{\guillemotright}
[0.05em]
{\guillemotleft}
{\guillemotright}
\MakeOuterQuote{"}
%\MakeAutoQuote{«}{»}
\end_preamble
\use_default_options true
\maintain_unincluded_children false
\language frenchle
\language_package default
\inputencoding utf8
\fontencoding global
\font_roman default
\font_sans default
\font_typewriter default
\font_math auto
\font_default_family default
\use_non_tex_fonts false
\font_sc false
\font_osf false
\font_sf_scale 100
\font_tt_scale 100
\graphics default
\default_output_format default
\output_sync 0
\bibtex_command default
\index_command default
\paperfontsize default
\spacing single
\use_hyperref false
\papersize default
\use_geometry false
\use_package amsmath 1
\use_package amssymb 1
\use_package cancel 1
\use_package esint 1
\use_package mathdots 1
\use_package mathtools 1
\use_package mhchem 1
\use_package stackrel 1
\use_package stmaryrd 1
\use_package undertilde 1
\cite_engine basic
\cite_engine_type default
\biblio_style plain
\use_bibtopic false
\use_indices false
\paperorientation portrait
\suppress_date false
\justification true
\use_refstyle 1
\index Index
\shortcut idx
\color #008000
\end_index
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
\paragraph_indentation default
\quotes_language english
\papercolumns 1
\papersides 1
\paperpagestyle default
\tracking_changes false
\output_changes false
\html_math_output 0
\html_css_as_file 0
\html_be_strict false
\end_header
\begin_body
\begin_layout Verbatim
\end_layout
\begin_layout Verbatim
"This is a quotation," he said.
"It continues onto the next paragraph.
\end_layout
\begin_layout Verbatim
\end_layout
\begin_layout Verbatim
Here is the continuation of my quote.
As per literary convention,
\end_layout
\begin_layout Verbatim
there is no end-quote at the end of the previous paragraph."
\end_layout
\begin_layout Verbatim
\end_layout
\begin_layout Verbatim
blabla
\end_layout
\begin_layout Verbatim
\end_layout
\begin_layout Verbatim
«This is a quotation,» he said.
«It continues onto the next paragraph.
\end_layout
\begin_layout Verbatim
\end_layout
\begin_layout Verbatim
Here is the continuation of my quote.
As per literary convention,
\end_layout
\begin_layout Verbatim
there is no end-quote at the end of the previous paragraph.»
\end_layout
\begin_layout Verbatim
\end_layout
\end_body
\end_document
Third point: I wonder if I could use \MakeAutoQuote{«}{»} with \DeclareQuoteStyle to be able to type «some text» in the LyX editor instead of "some text". I want to use «some text» instead of « some text », but of course still output « some text » when french style is selected in the preambul.
