Google "free forum hosting" (without quotes).
It is very, VERY unlikely that free webspace would allow anything else installed, so unless it already includes a forum, you will have to link to a free forum and put up with whatever garbage ads they shovel with it.
No-Ad Free Forum Hosting - FreeForums.org
Seems too good to be true? - free forum, no ads, from the description, it seems it survives on pro upgrades.
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Mary had a little lamb,
Her father shot it dead
Now Mary takes her lamb to school,
Between two crusts of bread