Flutter : Problem with FirebaseAuthException returning error in a variable - variables

Question

I would like to store the result of my error: FirebaseAuthException in my ERROR variable, located in my main file, but I can't. I leave you the code of my two files. Thanks in advance
Fonction:
Future signInWithEmailAndPassword({
required String email,
required String password,
}) async {
try {
UserCredential result = await FirebaseAuth.instance
.signInWithEmailAndPassword(email: email, password: password);
User? user = result.user;
return user;
} on FirebaseAuthException catch (e) {
String erreur;
if (e.code == 'user-not-found') {
erreur = "Utilisateur non trouvé";
} else if (e.code == 'wrong-password') {
erreur = "Mauvais mot de passe";
} else if (e.code == 'invalid-email') {
erreur = "Email invalide";
} else {
return null;
}
return erreur;
}
}
File with my function when my button is clicked.
I specify that I created an "error" variable in this file
onOkButton() async {
if (_formKey.currentState!.validate()) {
await signInWithEmailAndPassword(
email: mailController.text.trim(),
password: passwordController.text.trim(),
)
.then((value) => user = value)
.onError((error, stackTrace) => erreur = error.toString());
}
print(user?.email);
mailController.clear();
passwordController.clear();
isConnected();
}