What influence has he had on modern society?
Caesar reformed the Roman calendar from the old 355 day lunar calendar of the Roman to a 365 day calendar with a leap year evey 4 years... sound familiar? well it should the Julian calendar that he adopted (which because pretty standardized over the geographical span of the Roman empire) was used until Pope Gregory XIII updated it, in 1582, to be more accurate in regards to when leap days should be omitted. So the calendar you use today is just an updated version of Caesar's.
Caesar also conquered Gaul, modern France. So 500 years or so later once the Franks had the run of the place, you can bet the people who lived there were pretty culturally Roman. So the fact that the French language is a "Romance" language, AKA languages that are based on Roman Latin, is largely Caesar's doing.
These are just 2 big examples of Caesar's direct influence on today, but there are many many more things that he has directly and indirectly been responsible for. The man had a huge influence on later Roman history, which in Turn has left a long shadow of European and Western history as a whole...