TRESemmé is a brand name.
The brand name is a word play and reference to Edna L. Emme, then a leader and national spokesperson for the professional hair care industry.
Are you shure of the spelling?
If you're it's not an English word.
I know it's a hair product brand and tres does mean very but emme doesn't mean anything in French, at least not that I know of.
According to the wikipedia article about the company (hair care), the name is a play on words about a woman named Edna Emme who was a leader and spokesperson in the national hair care industry at the time the company was founded.
The explanation about "Emme" meaning the last name of the spokesperson of the national hair industry makes a lot of sense. Thanks for deciphering the big mystery. Tresemme simply means "very much Emme"....