Champagne does this by increasing the availability of nitric oxide, a vascular active molecule which controls blood pressure. It is able to induce these effects because it contains polyphenols, plant chemicals from the red grapes and white grapes used in champagne production.
When you drink champagne, these polyphenols get absorbed into the circulation where they are able to act on the vascular system. Specifically, they appear to slow down the natural removal of nitric oxide from our blood, meaning that it will have a longer time to act on blood vessels and so improve the flow of blood around the body.
Read more here: Champagne Is Good for Your Heart, Study Suggests