How should I deal with a sum of money I found in an airport in a European country while returning to my home country, knowing that I am not currently in the country where the money was found?

The ruling on a luqata (lost and found item) in non-belligerent disbelieving lands is the same as the ruling on a luqata in Muslim lands. Therefore, it is obligatory to publicize it for one year if the amount is such that people of average means would actively seek it. It is not permissible to claim ownership of it merely by picking it up. It is obligatory to publicize the luqata in the country where it was found, either by yourself, or by delegating someone else, or by handing it over to the authorities responsible for such matters. As for a luqata in belligerent disbelieving lands, it is owned by whoever finds it, and they are not obligated to publicize it, unless doing so would cause them harm.