Hi,
It would be very helpful if you could give us some names,dates and locations, then we could help you work backward to your ancestor.There are many Gregoire,brothers and cousins, who went to the States about 1800. Just in my tree, I count over two dozens posiibilities from various lines and generations. We have four ancestors we can connect to, three from France who arrived in the 1600's and one from Belgium, I believe, in early 1700's. They are not connected to Sweden up to the 1500's to my knowledge.
Most Gregoire changed their name for ease of pronounciation once they settled in the States,Gregor,Gregory,Grayware,etc.Gregiore is usually a typying error.
There is however a Swedish doctor,
Grégoire François Du Rietz, who was part of the Swedish nobility but he is not related to any Gregoire families in Canada. I believe some of his descendants did immigrate in the 1800's to the States.He used the name Gregoire as first name, a practice which was and still is used by the Gregoire's. By coincidence his middle name was Francois and this may be the connection to your family story as my ancestor was Francois Gregoire, of Languedoc, France was an army surgeon-barber who arrived in 1667. If you want to contact me directly, I'll be pleased to help if I can, cgregoire@sprint.ca