The annotations for these lines on Genius.com suggests a few potential explanations.
Annotation for "I've fallen in love/I've fallen in love for the first time".
The narrator says that he may have fallen in love with someone who’s not of the opposite sex. He may have had relationships with women before, but it wasn’t love, and therefore falling in love with a man feels like it’s the first time.
It could also mean that the narrator has lost feeling for his partner and has fallen in love with someone else. The reason it could be ‘for the first time’ is because the narrator hasn’t felt love for his partner in such a long time that when he falls in love again, it feels like it’s the first time.
Annotation for "And this time I know it's for real"
Again, the narrator may have had relationships with other women, however that love may have felt forced or unreal. Falling in love with a man feels like it’s real love.
The narrator could also be implying that his love for his partner could be fake and this time, him falling in love with someone else is real.
While these annotations are unverified, and only have a total of one upvote, at first glance the first explanation certainly seems to make sense. Queen lead singer Mercury began dating his long-term partner Jim Hutton around the time The Works, on which "I Want to Break Free" appeared was released, and up until that time had only really dated women publicly. There are also no gender specific nouns or pronouns in the song to identify the gender of the person to whom the narrator is expressing his love.
However, the song was written by John Deacon, not Freddie Mercury, and it also came out about before Mercury had started officially dating Hutton, so it's certainly possible that Mercury wasn't yet in love with Hutton. In addition, it appears that Mercury wasn't publicly out of the closet yet, though there was speculation. So I think it might be safe to rule this interpretation out.
This makes me think that the second interpretation is more likely, especially given the lyrics in the first verse of the song:
I want to break free
I want to break free
I want to break free from your lies
You are so self satisfied I don't need you
I have got to break free
God knows, God knows I want to break free
Note the third and fourth lines, which I've bolded. It seems like the narrator is saying that the person who he is currently with keeps lying to him, and he doesn't want to be with them anymore, so he wants to break free. He then lets that person know that he's fallen in love, and this new person is someone who won't lie to him and isn't selfish, so this time it feels like real love. It's a stab at the unsatisfactory relationship that the narrator is currently in.
This is my interpretation, obviously it could be wrong. I think @SovereignSun's interpretation is possible as well. It's possible that the only way to truly know what the lyrics mean is to contact John Deacon himself.