Bonjour Ankit,

‘Fut’ is Le Passé Simple of ‘être’ whilst ‘fit’ is Le Passé Simple of ‘faire’.

In this particular sentence, ‘ to be careful to do [sthg]’ is translated with the French expression ‘faire attention à + [sthg]’. Therefore you are looking at conjugating the verb ‘faire’ in Le Passé Simple, as per the topic of this lesson.

See following link: recognise-etre-in-le-passe-simple

I hope this is helfpul.

Bonne journée!