Touch file /tmp/existing.fxml on your system.
Then run the code below and in the File Chooser dialog enter 'existing' without the file extension.
Press Save button: on Mac and Win you get an overwrite confirmation dialog, then if you confirm the file returned is /tmp/existing.fxml.
On Linux you get no overwrite confirmation dialog and the file returned is /tmp/existing, the extension part is missing.

package javaapplication1;

import java.io.File;
import javafx.application.Application;
import static javafx.application.Application.launch;
import javafx.stage.FileChooser;
import javafx.stage.FileChooserBuilder;
import javafx.stage.FileChooser.ExtensionFilter;
import javafx.stage.Stage;

public class JavaApplication1 extends Application {

    @Override
    public void start(Stage primaryStage) {
        FileChooser fileChooser = FileChooserBuilder.create().initialDirectory(new File("/tmp")).extensionFilters(new ExtensionFilter("fxml", "*.fxml")).build();
        File ignored = fileChooser.showSaveDialog(primaryStage);
        System.out.println("File returned by chooser is " + ignored);
    }

    public static void main(String[] args) {
        launch(args);
    }
}