how in a calculation do I specify the value of a single checkbox?
If you want to determine if "French" was clicked in the above example no matter what other boxes might be clicked, use:
Not IsEmpty ( FilterValues ( YourCheckBoxFieldHere ; "French" ) )
This result will be True if the French value has been selected.
And there are ways to use the List function if you want to use a script to select a value in this field without clearing the other check boxes as well as ways to clear just the one selected value.
"Other..." will be a problem. You might consider putting "other" values in a separate field or set up this value list with a "use values from field" value list and add a new record to that table with the new value--which then adds the value as a check box in your check box group. (This takes a script performed when the user clicks a check box in this group.)
You may find it helpful to look at: Adventures in FileMaking #2 as some of the topics in it cover both how check boxes work, how to use them in calculations and also shows some alternative setups that look and function like check boxes, but aren't. (And have added features not possible in a standard check box group.)