Television adapter

this might be useful - https://www.sony.com/electronics/support/articles/00006701

Presumably, the television in the motor home will be 240 volts or 12 VDC, and you won't need a converter. If that's not the case, even with a voltage converter, a U.S. model television won't really be satisfactory for European television programs.

I would buy one in Europe and save myself the hassle of taking one and having to get all the necessary equipment. Smart TV sets cost from €100 and up nowadays, so they are not that expensive, especially considering that a motorhome rent for 5 months will probably cost you about €15,000-25,000 depending on the size.

Besides an electric converter to convert 240V to 110V (a good one otherwise you will fry your TV) unless your set can handle both voltages (in which case you just need an adapter), you will need an HDMI video format converter to convert the European signal to the American NTSC standard (Europe uses the PAL or SECAM standard depending on the country). The HDMI converter is necessary to see local broadcasts or local cable or satellite tv. Without an HDMI converter you can connect your TV to the internet and steam via its apps. That should work, however there maybe restrictions on your ability to downstream US content abroad. For example my wife was unable to see some of the PBS contents by streaming it because of country restrictions. You might be able to get around that by using a VPN service which makes your device to connect to a US based Internet IP address while abroad. I use that VPN to see European soccer games in the US which would not be otherwise streamable overseas, there are several VPN service providers in the market.

Before someone else posts the question, I presume you have EU citizenship (or immigrant visa) to travel in the Schengen area over the 90 day period limit.

Other options would be to stream your programming instead of putting up an antenna. You could play around with VPNs and such to watch what you want wherever you are.

I would also think a rental RV would have a TV in it, or just go to a discount store and buy one and then leave it behind. They're just commodities these days, quite cheap. They sell them in the checkout line at my local supermarkets.