I believe a language course must be included in section 6F regardless of the course being run as LINC/CLIC or ESL, as per the instructions on the form itself (see below). However, you should clearly identify it was a "language course" that you attended so as to avoid any confusion.
You are not required to submit proof of attendance to document your language training as part of your education history (see the quote from the Application Guide below). Yet if you use a language course as proof of you language skills in Section 7 of the application form, confirmation of completion must be submitted.
Application form, Section 6F:
A) Have you worked in the last four (4) years?
B) Have you attended an educational institution in the last four (4) years or participated in English/French language training?
If you answered yes to questions A) and/or B), list your work and/or education history [...]
Application guide, section 5, Question 6F:
You must list all your work and education history including English/French language training for the past four (4) years and must account for each month.
Application guide, section 4 Education Records:
The education records must cover each calendar year, if applicable. It is sufficient to submit one official education document per calendar year of schooling during the relevant four (4) year period. Note: You are not required to submit proof of attendance at English/French as a second language training programs.