Here is the fragment again:
To enjoy the warm sunshine that he could see spilling through the blinds.
You correctly identified the fragment as an infinitive phrase. To enjoy, the infinitive that begins the phrase, is the clue.
To fix this fragment, you could add a subject and verb, like this:
Emmanuel wanted to enjoy
the warm sunshine that he could see spilling through the blinds.
Or you could use Punctuation Rule 5:
Main Clause + Ø + Infinitive Phrase.
The correction would look like this:
Emmanuel wanted to escape the classroom
to enjoy the warm sunshine that he could see spilling
through the blinds.
Or you could use Punctuation Rule 6:
Infinitive Phrase + , + Main Clause.
And the correction would look like this:
To enjoy the warm sunshine that he could see spilling
through the blinds,
Emmanuel anticipated his escape from the classroom.
Enjoy becoming a member of the royal court!