J is in fact a much more recent invention than many of us would suppose[0]. It is worth adding, however, that it would not have saved G, except in English; our pronunciation of J, while close to the French and a couple others (with an added /d/ at the front), is quite unique among languages that were written in the Roman alphabet at the time.

In any case, English suffers quite a few more more overloaded consonants that C and G. Most occurrences of /z/ (a frequent sound in English) are marked with an S (codes), and a great many /t/ sounds are written D (typed).

[0] https://en.wikipedia.org/wiki/J#History