What is the ruling on drinking barley beverages such as "Fayrouz" and "Birell" if the manufacturing company also produces alcoholic beverages?

If it is confirmed that the two aforementioned drinks are free from intoxicants, then there is no objection to drinking them. The basic principle regarding things is permissibility. The fact that companies sell unlawful things does not prevent dealing with them in permissible matters. It has been the practice since the time of the Prophet, peace and blessings be upon him, that it is permissible for Muslims and non-Muslims to buy and sell from each other in matters that are lawful.