An ancestor of mine emigrated from Luxembourg to the United States in the mid-19th century. His last name was French and his family background was in Lorraine. How common were French-speaking immigrants from or near the Low Countries in the US in this period?

Can't answer that quantitatively- don't know all the US immigration statistics. But there were a number of Walloons who ended up in Door County, Wisconsin circa 1850 and formed a remarkably durable community, keeping their particular language for a very long time: it's a different French dialect from Parisian or Quebecois French. As a result, they've gotten some study.

The University of Wisconsin has a website of some sources on this Belgian immigration.

https://uwdc.library.wisc.edu/collections/wi/belgamrcol/

One small study here has found that in 1856 upwards of a thousand emigrated into the upper midwest through Chicago, Milwaukee, Green Bay and sometimes came there after landing in Canada.

Jean Ducat : Passegers Belges Partis vers L'Amérique en 1856

Another paper here says that Luxembourgeois came into western New York circa 1820-1840, and from there moved into Ohio and Indiana, and that Luxembourgeois and Belgian Lorraines also came into the midwest in the following decades.