I would probably say "expand your horizon (or perspective) by learning English." "Widen your gaze" sounds slightly unnatural in this context, particularly since it means more or less "open your eyes and look more carefully." It also sounds slightly archaic, like something a character from a nineteenth century novel would say.

This does not sound right in English. In America, it is common to talk about broadening your horizons. To broaden means to make wider, and the horizon is the absolute furthest point we can see when looking at the setting sun for example. "Broaden your horizons by learning English" would sound better.