You must know what you actually want to do after completing your Bachelor's degree.

If you are pursuing B.Com honours and your GE is English,then it doesn't mean you would have less opportunities compared to those whose GE is Economics.

It's all about what you aspire to do in future.

If you want to go in finance or banking sector,Economics may be an add-on but it doesn't vouch for you getting throuh such entrance examinations.

B.Com gives you exposure to the fields of Multimedia,media, public relations etc and studying English mouls your perspective in many ways.Also,it will be helpful if you aspire to go for MA in English and can become a professor. 

Moreover,it's not your GE but your hard work and right approach defines how you make use of the opportunities that come your way.

Stay positive!