Update doc

_pkgdown.yml

@@ -59,12 +59,6 @@ template:
             if (item.textContent === "Reference" || item.textContent === "Fonctions") {
               item.textContent = lang === "fr" ? "Fonctions" : "Reference";
             }
-            
-            var home_url = document.querySelector(".navbar-brand[href='index.html'], .navbar-brand[href='fr_index.html']");
-            if (home_url) {
-              if (lang == "fr") home_url.href = "fr_index.html";
-              else if (lang == "en") home_url.href = "index.html"
-            }
           });
         }
         
@@ -84,34 +78,43 @@ template:
           window.location.href = current_url;
         }
         
-        function initializeLanguageSelector() {
-          var languageSelect = document.getElementById("language");
-          if (languageSelect) {
+        function initialize_language_selector() {
+          var selected_language = document.getElementById("language");
+          if (selected_language) {
             var selectedLanguage = localStorage.getItem("selectedLanguage");
             if (selectedLanguage) {
-              languageSelect.value = selectedLanguage;
+              selected_language.value = selectedLanguage;
             }
             change_language(selectedLanguage);
           }
         }
         
         document.addEventListener("DOMContentLoaded", function() {
           
-          var languageSelect = document.getElementById("language");
-          if (languageSelect) {
-            languageSelect.addEventListener("change", function() {
+          var selected_language = document.getElementById("language");
+          if (selected_language) {
+            selected_language.addEventListener("change", function() {
               localStorage.setItem("selectedLanguage", this.value);
               change_language(this.value);
             });
           }
-
+          
+          var home_url = document.querySelector(".navbar-brand[href='index.html'], .navbar-brand[href='../index.html'], .navbar-brand[href='fr_index.html'], .navbar-brand[href='..fr_index.html']");
+          if (home_url) {
+            if (selected_language.value == "fr" && !home_url.href.includes("fr_index.html")) {
+              home_url.href = home_url.href.replace("index.html", "fr_index.html");
+            } else {
+              home_url.href = home_url.href.replace("fr_index.html", "index.html");
+            }
+          }
+          
           window.addEventListener('storage', function(e) {
             if (e.key === 'selectedLanguage') {
-              initializeLanguageSelector();
+              initialize_language_selector();
             }
           });
 
-          initializeLanguageSelector();
+          initialize_language_selector();
           
           var observer = new MutationObserver(function(mutations) {
             mutations.forEach(function(mutation) {