The opposite will actually happen. The rise of renewable energies will decrease energy cost dramatically. In some countries solar generation is already cheaper .
energy is highly regulated market, so I dunno, but in general, increased demand increases price, unless supply grows to meet demand (and there is a competitive market to drive down prices). So more EVs, more demand for electricity, and less demand for gasoline, so former might become more expensive, and the latter cheaper. what actually will happen is going to depend on long term investment decisions, changes in tech, and the specifics of industry regulation (which I'm mostly ignorant of)