fix french homepage

apps/homepage/src/components/app-shell/AuthHeader.tsx

@@ -1,6 +1,7 @@
 'use client';
 
 import { localizedPath, locales, type Locale } from '@/lib/localization/config';
+import { persistLocale } from '@/lib/localization/client';
 import { persistTheme, themePreferenceEvent } from '@/lib/theme/client';
 import { type ThemePreference } from '@/lib/theme/config';
 import Image from 'next/image';
@@ -62,6 +63,7 @@ export function AuthHeader({ locale, themePreference: initialPref }: Props) {
 
   const switchLocale = (next: Locale) => {
     setLocaleOpen(false);
+    persistLocale(next);
     const segments = pathname.split('/').filter(Boolean);
     if (segments.length >= 2) segments[1] = next;
     router.push('/' + segments.join('/'));

apps/homepage/src/components/app-shell/HeaderRouter.tsx

@@ -3,6 +3,7 @@
 import { usePathname } from 'next/navigation';
 import { SiteHeader } from './SiteHeader';
 import { AuthHeader } from './AuthHeader';
+import { routeIdFromPathname } from '@/lib/localization/config';
 import type { ShellMessages } from '@/lib/localization/messages';
 import type { Locale } from '@/lib/localization/config';
 import type { ThemePreference } from '@/lib/theme/config';
@@ -15,7 +16,8 @@ interface Props {
 
 export function HeaderRouter({ locale, messages, themePreference }: Props) {
   const pathname = usePathname();
-  const isAuth = pathname.endsWith('/sign-in') || pathname.endsWith('/forgot-password');
+  const routeId = routeIdFromPathname(pathname);
+  const isAuth = routeId === 'sign-in' || routeId === 'forgot-password';
 
   if (isAuth) {
     return <AuthHeader locale={locale} themePreference={themePreference} />;

apps/homepage/src/components/app-shell/SiteHeader.module.css

@@ -61,6 +61,7 @@
   color: var(--text-primary);
   font-weight: 650;
   text-decoration: none;
+  white-space: nowrap;
 }
 
 .navigation a {