A few days ago, I received a request for the identification of a Honda C70 and this is the outcome:
Your statement about this motorcycle is as follows: You declare that the frame number is C70-803xxxx and the engine number is similar except for the C70 part. You have a round headlight, 6 volts and no electric starter.
EXPLANATION AND IDENTIFICATION:
Your statement of the engine operating on 6 Volts: This means that your engine has contact breaker point and therefore your engine originates from somewhere between 1972-1981. From 1982 on, the operating voltage was 12 volts and the ignition was done by CDI. 
Your saddle is a two-tone saddle which belongs to a C70C and C70E models. 
The specific attachment of the passengers leather handle grip indicated that this belongs to a 1982 or 1983 C70 Passport. 
The problem here is that your frame number does not match with this model, nor does the fact that you have ignition breaker points and not CDI as the Passport has.
Your frame number has a match for a Honda C70C. This model has been produced between frame number C70-8022434 and C70-8039828 
“The C70-C models are easily distinguished by their two-tone dual seats and restyled headlamp cowling and leg shields.” Restyled does not mean square, but since there is only round or square, I cannot give a clear statement on that.
Warnings: You declare that the frame number and engine number are identical (in number). This is basically impossible. Until this day, I have not ever seen a matching number and the production of frames and engines happened separately. They can be close though, but matching is something I find hard to believe.
 Clymer Honda 50-110cc OHC Singles, 1965-1992, Page 230, left column, first paragraph.
 Haynes Honda C50, C70 & C90 Owners Workshop Manual, Page 126, second column, first paragraph.
 Honda Motorcycle Identification Guide, Page 30, 2nd and 3rd model.
 Haynes Honda C50, C70 & C90 Owners Workshop Manual, Page 127, first column, first paragraph.