Genes are the regions of DNA that code for particular enzymes, proteins, etc. It is at the level of gene transcription followed by translation in the ribosome in which we get expressed proteins. Thus, the relationship between genes and enzymes is that genes code for enzymes. It can get a little confusing, especially since there are enzymes that help translation occur, and other proteins get involved in the process as well. There are several articles and books that have been published in the past decade that outline and explain this relationship. Hope this helps!
I think if you have a gene sequence jus translate it using expasy tool of protein translation and do protein blast.... it will give you the idea of the domains presents in your protein/enzyme and thus will give you idea about function of the enzyme.....
i suppose i have correctly given answer for your question...