dynamic-recaptcha-language-per-form.php

<?php

add_action( 'nf_get_form_id', function( $form_id ) {
  if( '12' == $form_id ) {
    $recaptcha_lang = 'en';
    Ninja_Forms()->update_setting( 'recaptcha_lang', $recaptcha_lang, true );
  }
});

dynamic-recaptcha-language.php

<?php

add_action( 'init', function() {
  if( true ){ // Some condition to change the language.
    $recaptcha_lang = 'en';
    Ninja_Forms()->update_setting( 'recaptcha_lang', $recaptcha_lang, true );
  }
});

update-recaptcha-language.php

<?php

/**
 * Update the `recaptcha_lang` setting.
 *
 * @param string $setting_key
 * @param string $new_value
 * @param bool $defer_update True will update the value in memeory, but will not update the database.
 */
Ninja_Forms()->update_setting( 'recaptcha_lang', $recaptcha_lang, true );