The poll of 246 MPs found that 62 percent would support such intervention, Radio-Television Suisse said on its website on Tuesday.
The poll was taken after the cantonal parliament of German-speaking Thurgau in August decided to drop French classes from its primary schools in favour of English.
The government in the canton of Nidwalden followed suit and other German-speaking cantons are considering similar measures.
Switzerland has three official languages — German, French and Italian — although the majority of the population speaks a German dialect.
According to federal statistics from 2012, 64.9 percent of the population speaks Swiss German or German as their main language, followed by French (22.6 percent) and Italian (8.3 percent).
English was identified as the main language of less than five percent of the population.
However, government figures show that at work English is spoken by 17.7 percent of employed people.
And English is increasingly becoming the second language of choice for residents in both German- and French-speaking parts of the country.
But the dropping of French in schools is causing concern among residents in the French-speaking cantons, who fear this could hurt the country’s unity.
In the poll, 81 percent of Francophone and Italian MPs supported the idea of federal intervention to support teaching of a second national language, while just 52 percent of German-speaking MPs were in favour.
Despite concerns about the future of French in Switzerland, the percentage of French-speakers has steadily grown from 18.7 percent in 1970 to 22.6 percent in 2012.
A clear majority (57 percent) of MPs surveyed backed the teaching of English in addition to a second national language in public schools, while only 35 percent supported the instruction of a second national language without English.