Using Google Maps I found the Zenith and asked for hotels locally. These might be a starting point:

Campanile Hôtel, Limoges Nord
Hôtel du Parc
Bienvenue Hôtel

They are all in the postcode area 87100, and all have websites. They are the nearest to the venue, and should be ok but not very traditional, rather more minimalist!

As the Zenith is approached by various dual carriageways, walking may not be very easy and you might need to consider renting a taxi ................

I could not check availability - lack of time sorry - nor prices, but they should be reasonable if they don't add supplements for special events on at the Zenith. At least this is somewhere to start!! Good hunting!

Many thanks Als! I'll get Googling this afternoon!