Here in France I do dance without a partner, as is common here. I can't speak for Freestyle, but there are two adult dance competitions/year.
I'm in the process of helping translate the competition announcements, with the hope that more people from your side of the channel will come and participate. Here's how it works:
The dance competition is open to all levels, from Preliminary on up, solo and couple. Solo ice dance is just like freestyle with some terminology changes (combo spin means change of foot, not change of position) and no jumps over 1/2 revolution.
Preliminary and Preparatoire (dunno if this category exists in the UK, it does not in the US where I'm originally from) can compete in pattern dances only. Pre-bronze on up can compete in pattern and free dance.
All you have to do is get the announcement, which I'll be happy to share here, or you can join the Coupe des Druides group on Facebook (you won't be the only anglophone member, promise) and you'll be in the loop for the Coupe des Druides which happens in late January and the Fontenay Cup at the end of April. They change cities, but lately Druides has been happening in Toulouse and Fontenay in the Paris region. I competed for the first time this year and had a total blast. It's a great atmosphere, and really friendly. There is a general consensus that more participants from the UK would be very welcome.
I can not speak for Freestyle (which they call artistic skating here), as that is actually run by a different sub-organization of the French equivalent to NISA, so even the clubs are different.
Its up to each competitor (or one representative of your club if a group are going) to fill in the forms and make the arrangements to come. There is help for the asking with getting that done if you're in the facebook group.
As for acquiring the skills to be competitive, all you need to do is learn the pattern dances that are being competed. Once you move up to/ feel comfortable entering a level where you can present a freedance program, you need to know what the elements are and how to legally put them together. That's a bit more complicated, but also something your coach can help you with.
I would say just do it! Adult competitions are fun and you'll meet lots of new friends.