'My heart is on the floor' means that I feel in very low spirits (sad, downhearted, discouraged, depressed, demoralised, dejected). We say 'my heart sinks' when facing a situation where we expect to fail, or 'her heart soared' to express happiness or hope. Another phrase you may hear is 'his heart was in his boots', meaning that he was feeling very sad or fearful about something. (The idea here is that his boots are at the lowest point of his body, so his heart has fallen to the lowest possible position.) In this context, my first guess would be that she is suffering from unrequited love or has been rejected by the man (i.e., 'you have broken my heart') or fears rejection by him. Another possibility is that she is declaring her love for him, using the metaphor of her heart being on the floor to express her abject helplessness in the face of overwhelming emotion, or to express the idea that he has conquered her, and her heart now (metaphorically) lies at his feet.

it's not common. I wouldn't try using it in every day conversation. even native speakers might not understand

I assume she likes him? To floor somebody is to overpower somebody. So i guess she is overwhelmed by him. But this expression is strange - I have been speaking english fluently for years and have not encountered it. So i think you can let it pass, you probably won't hear it again soon.