Is it permissible to eat non-halal meat available in European markets, given that there are Arab markets selling halal meat, but it is expensive and its source is questionable?

It is not permissible to eat meat that is certainly known not to have been slaughtered according to Islamic law, or if there is doubt about whether it was slaughtered according to Islamic law, except in cases of necessity. As for meat that is certainly known to have been slaughtered according to Islamic law by a Muslim or a person of the Book, there is no harm in eating it. The high price of permissible meat is not an excuse to eat that which is forbidden.