教(as a verb) + object[+complement,if any]
So, let's see the following examples,
教 + (英)语 => teach the language which is used among English(American) people.
教 + (法)语 => teach the language which is used among French people.
教 + (英语是第二)语 => Mandarine speakers may wonder what "英语是第二" is.
Here, you may have two options to make the sentence more clear.
1. I teach the "English Is The Second Language" program online.
2. I am the teacher of the "English Is The Second Language" online program. (Imply that you can teach the program)
Otherwise, you need to keep the "ESL" as it is. I mean, the abbreviation form.
For example,
我(通过在线方式)教授ESL。
or
我是ESL的老师。
In addition, Mandarin speakers are used to naming something/somebody with nouns or the composition of determiner and noun(s).
As a result, “英语是第二”语 doesn't conform to the rules of naming shown above.