When you are using WooCommerce with WPML usually the stock is in sync between products, but do I understand right, that you are not using WC and instead you are handling a CPT of products that uses product details based on ACF?
Please try to set this stock field to "copy" but take note that this will only allow copying of the field value when translating a product.
This means you will need to update the translations in order to have a similar stock.
Possibly running an import for the translated products would be advisable in this case.