Actually she sings: "Je rêve
en grand" which literally is "I dream
in big" but I'm pretty sure that it means nothing in English.
If it does, then use it! Unless it's not the same: another example in French, you can also say "voir les choses en grand", literally "see things in big". A good trick to get it in English I think: add a word like format, dimension. "I dream/see things in big format", in big dimension, etc...
It's exactly the idea even though this notion is not implied!
Now that I re-read it:
Moi, j' rêve en grand
Comme l'éléphant
Je rêve immense
"Comme l'éléphant" goes with the 3rd line above and not the 1st.
I already said that it means that "just like the elephant (does), she dreams immense"