System.getProperty("line.separator");

FileChooser fc = new FileChooser();
    FileChooser.ExtensionFilter filter = new FileChooser.ExtensionFilter("txt files (*.txt)", "*.txt");
    fc.getExtensionFilters().add(filter);

    File file = fc.showSaveDialog(null);

    if (file != null) {
        try {
            PrintWriter write = new PrintWriter(file.getAbsolutePath());
            write.print(OutputText); // где OutputText нужный мне string
            write.close();
        } catch (FileNotFoundException fileNotFoundException) {
        ...
        }
    }