Congratulations on your Solex! What Ed says is true, the 3800 came out in 1966. But you may have a hard time looking up your serial numbers. There are no records for the Solexes sold in America, Canada and most other export countries. The charts on the French sites are for the bikes sold in France for the most part. Most of the 3800 Solexes sold here have serial numbers that begin with a 5 and if you look that up on a French chart, it will tell you that you have a Micron. Also, Solexes like the 4600 were never even sold in France even though they were manufactured there. They have virtually no information on the 4600 over there. I have been keeping track of the Solexes sold here and can tell you the date of manufacture by knowing either the seven digit motor serial number or frame number that Ed mentions. A picture would be helpful also.
Don't be fooled by the 14-3-1966 date that may be cast into the top of the motor. It is not the date of manufacture, but the date that the motor type was presented for approval, (date of homologation).
Please get back to me with the serial numbers and a photo if possible and I'll tell you everything I can about your particular Solex. And don't hesitate to ask any questions that you might have.
ps the dates on many of the photos of Solexes in the photo section are incorrect. For the reasons mentioned above, many people have a hard time telling exactly what they have.