I have German Palatine ancestors that moved to South Carolina in the early 1700s as well as a Frenchman, probably Huegenot, who moved to Virginia along with some brothers/cousins. The original immigrants were indentured servants who had to work off the passage and the right to settle land through that servitude.
In addition, England allowed some Protestants to move to England and to Northern Ireland during the same periods. Some of those anglicized their surnames and some of their descendants later moved to America. At least one branch of my family tree were probably German origination (Fike is NOT an English or Irish name) who were allowed to live in Ireland and who later moved to the Americas. My husband has a branch who were French Protestants who lived in a French enclave in England. His direct ancestor and some of his siblings later moved to Maryland - proven by another sibling's will in England when she left property to their children.
Another route for introduction of Germanic and French genes was the Quaker migration - many had moved to the Netherlands during the persecutions and some married local people. When they or their children later moved to the Americas, they brought those genes with them. Quite a few Quakers moved from Pennsylvania to the Carolinas - some in order to spread the Quaker beliefs, some (as my ancestors) because they were more activist against the British and had been evicted from their Quaker communities. My main ancestor who moved from Pennsylvania to North Carolina was one of the Regulators who protested and fought against the British rules before the American Revolution.
England just wanted to get settlers to hold land - and in the Southern colonies, there was a massive death rate from introduced diseases such as malaria and yellow fever - first among the indigenous populations, then among the Northern European colonists. This is one reason that African slaves became the main work force - many came from regions where those diseases had been endemic long enough that they had either genetic resistance or acquired immunity to them.
My Ancestry results:
Great Britain 38% - England, Scotland, Wales
Europe West 28% - Belgium, France, Germany, Netherlands, Switzerland, Luxembourg, Liechtenstein
Ireland/Scotland/Wales 27% - Ireland, Wales, Scotland
Low Confidence Regions:
Finland/Northwest Russia 4%
Scandinavia < 1%
Europe South < 1%
Asia South < 1%