Why eo_get_the_content/eo_get_the_excerpt don't exist ?

No, you use WordPress’ native the_content() or get_the_content(). (Though the former you can’t use ‘outside’ the loop).

So how do you bring up the contents or extract and the thumbnail?

<?php
		$events = eo_get_events(array(
                    'numberposts'=>-1,
                    'tax_query'=>array( array(
                         'taxonomy'=>'event-category',
                         'operator' => 'IN',
                         'field'=>'slug',
                         'terms'=>array('photos','petite-enfance-2')
                         ))));?>

			<?php if ( have_posts() ) : ?>

			<header class="archive-header">
				<h1 class="archive-title"><?php printf( __( 'Photos de la petite enfance: %s', 'twentyfourteen' ), single_cat_title( '', false ) ); ?></h1>

				<?php
					// Show an optional term description.
					$term_description = term_description();
					if ( ! empty( $term_description ) ) :
						printf( '<div class="taxonomy-description">%s</div>', $term_description );
					endif;
				?>
			</header><!-- .archive-header -->

			<?php
				// Start the Loop.

if ( $events ) {
	foreach ( $events as $post ) {
		setup_postdata( $post );
		the_title();
		the_post_thumbnail ();
		the_excerpt();
	}
	wp_reset_postdata();
}

					// Previous/next page navigation.
					twentyfourteen_paging_nav();

				else :
					// If no content, include the "No posts found" template.
					get_template_part( 'content', 'none' );

				endif;
			?>

I do not understand why it works, can you explain please ?

See this post: https://stephenharris.info/get-post-content-by-id/.

From memory you need to declare global $post; when using stuff like the_content() outside the loop. (Not sure about excerpt).

Thank you to you for your response speed. Sincerely, good luck to you and your plugin