Born in Rosiere,
Hello there and welcome to DC. You bought a Baumalu pot, made in Alsace, France near the border with Germany.
As Andy recommended, you should handwash this piece, I own several ones (three sizes like the one you describe) and clean them by hand right after using.
It is possible the detergent affected the color of the tinning, if you want to bring it back (tin it will darken with use) clean the inside by hand with a paste made with a small amount of lemon juice plus baking soda.
You can clean the outside with a similar paste, but is easier with a mix of table salt and lemon juice/white vinegar.
Have you removed the varnish from the cooper before using it?
This is done with a small piece of cotton soaked with acetone and a soap and warm water rinse afterwards. Perhaps the varnish affected the tin color.
Retinning costs approx. $5 per inch plus shipping. To define the size of your pot, you measure the diameter plus two times the height. This is what shops normally use to define their cost.
I couldn't find a shop near where you live, I'd check with your local Williams-Sonoma store. They normally have a listing of these type of craftsmem.
There are places in Colorado and New Jersey, here are the links:
Retinning and Polishing Copper Cookware for more than fifty years
Cookware Retinning and Metal Refinishing
Copper Cookware Retinning