Actual aircon units are quite cheap these days eg this 480 euro
https://www.amazon.fr/KLARSTEIN-Windwaker-Smart-Split-Climat... Not sure about the installation. Maybe you could DIY? I was thinking of it in London and imagine the installation will be more than the units.
One thing I can't work out is if something like that - a heat/cool aircon unit counts as a heat pump from the point of view of getting a government grant?