Yes. An L-2 spouse is employment-authorized incident to status, which means the spouse can work without a separate employment authorization document once admitted in L-2 status. Children in L-2 may study but not work.
Use the spouse's authorization deliberately
Since USCIS treats L-2 spouses as employment-authorized incident to status, the spouse's admission record is the key document, and it should show the L-2S annotation that employers accept for Form I-9. Confirm the annotation at admission rather than discovering it is missing at a job interview. The spouse's work can be for any employer, including continuing a remote arrangement with a Québec client, but the household should look at Canadian and U.S.
tax residence consequences before assuming a remote job simply continues. Children hold L-2 status as dependants until they turn 21 or marry; they can attend school and cannot take paid work. Plan the timing so that a child close to 21 is not left without status mid-year.
Each dependant's application needs proof of the relationship, with translations of any French civil-status documents.