I'm no polyamory expert, but looking at it from here I notice that this polyamory thing was forced on you. It was either that or hit the bricks. I get the impression you went along with it simply to be able to hold on to her.
By invoking polyamory, she was able to avoid a messy scene and be branded as a cheater. Now it's your problem.
She said she's not attracted to you anymore. I'm not sure it's realistic to say she didn't mean it. She said it. And her reluctance to have sex with you is the actions behind the words.
You've been edged out. He moved into your bed and is banging your girlfriend every chance they get. Now they're going to Paris (this is where I currently live) which is THE most romantic city on the planet. Then they're moving in together.
She's promising sex with you in the next 3 months? I believe she's hoping you'll be gone for good by then.
I suggest you recover the little dignity you have left and get out. Or in the very least, get yourself another girlfriend for those long dry spells with the current one.