To add to the answer already given, demographics play a large role in whether or not settlers learn the language of their destination. Are the settlers the majority? Then they might not have to learn the language. But if the incoming settlers are a minority, then some type of communication is going to be necessary. So for example as a rule for traders would learn to speak local languages, as not only were they a minority, but local languages were the language of business. In places where settlers were the minority, by the second generation their children wouldn't be learning these languages, they would speak them as mother tongues. This might last for many generations.

Another factor is the existence of pre-existing lingua francas. Cree was the lingua Franca of the Canadian prairies. American plains sign language was the lingua Franca large areas of the prairies and into the Rockies in places. And post contact, Chinook jargon was the trade language of the Pacific Northwest. And these locations it was more common for settlers to learn the lingua Franca than for them to learn specific local languages. And the same is true for indigenous populations, when lingua Frances were common, they would expect incoming settlers to learn to speak that lingua Franca rather than trying to learn the language of newcomers to their territory.

Again, in places where contact continued and assimilation was not the rule, many generations could go by with people speaking each other's languages. Multilingualism was the norm in such places for example within the broader Metis community of the Canadian west. In contrast, in places where displacement was the goal, language learning was often very minimal.

I am not an expert, but I think it really depends on time and place. In some very diverse and disparate eras and geographies, a lot of settlers probably would’ve spoken native languages; move over a century or five hundred miles, and that might not be the case. For example, jn what is now Quebec (certainly up to the late 18th century, but I don’t know about the 19th century), many different types of people spoke Indigenous languages: traders, clergy, and the host of people that come with those types of people certainly spoke Algonquin or Ojibwe. In a very material way, the existence of settlers in Indigenous lands depended on Indigenous people for their way of life. Interaction was not only common, but part of the texture of the everyday. Merchants took indigenous wives and lived in Indigenous communities. I’m blatantly stealing from Wikipedia here, but see “Van Kirk, Sylvia (1987). "The Role of Native Women in the Creation of Fur Trade Society in Western Canada, 1670–1830” who “calls them [Indigenous and Métis women married to European fur traders] ‘the basis of a fur trade society.” I can’t speak with confidence to demography, but I would bet that there were as many or more Native people in those lands as there were settlers. This is not exactly related, but the story of Kateri Tekakwitha, a Mohawk-Algonquin saint, is an excellent example of the level of inter-community exchange and contact. Indigenous people and settlers lived together; often in unequal, exploitative, and violent relationships, to be sure.

However, it is my understanding that in the time and place you suggested, the relationship between settlers and Indigenous people had become effectively genocidal. Take the Buffalo slaughter: this was a post civil war, Union General led, decades long, deliberate and explicit attempt to destroy the food system of Indigenous Plains peoples. Genocide, I think it is fair to say, is usually not conductive to language exchange.

I will add sources later, I swear to god.

Edit: for clarity, and now with source cited.

For a really accessible secondary source on the close relationships between First Nations people and settlers in “French Canada” see Susan Sleeper-Smith, “Encounter and Trade in the Early Atlantic World” in the collection “Why You Cant Teach United States History Without American Indians.” She looks specifically at the fur trade and reframes the colonial relationship, commenting on how Europeans in fact competed and undercut one another to produce goods for a highly discerning customer base that they relied on for survival: “Rather than marking a disruptive intrusion of foreign objects, the fur trade in reality involved Europeans producing ‘Indian goods’ for an Indian clientele.”

source on Buffalo slaughter:

From an 1869 issue of the army navy journal: “the quickest way to compel the Indians to settle down to civilized life was to send ten regiments of soldiers to the plains, with orders to shoot buffaloes until they became too scarce to support the r*dskins.” [censorship mine lol they obviously use the actual slur in the 1869 article] Another quote from Lieutenant General Schofield speaks even more bluntly: "With my cavalry and carbined artillery encamped in front, I wanted no other occupation in life than to ward off the savage and kill off his food until there should no longer be an Indian frontier in our beautiful country”

Smits, David. “The Frontier Army and the Destruction of the Buffalo: 1865-1883.” The Western Historical Quarterly, vol. 25 no. 3, 1994.