Learn French: Le forgeron a raté l'épée, faute d'utiliser le soufflet. - The blacksmith ruined the sword, for lack of using the bellows.

The preposition faute de (for lack of) can be followed by a noun or an infinitive. We use the infinitive here because the person doing the action is the same as the subject of the main sentence (le forgeron). You cannot use faute de with a conjugated verb, so a construction like faute qu'il utilise does not exist.

Could I rewrite this sentence using a noun after faute de instead of an infinitive?

Yes! Since faute de can take either an infinitive or a noun, you could say faute d'utilisation du soufflet (for lack of use of the bellows) or simply faute de soufflet (for lack of a bellows). Both alternative options are perfectly natural in French.

I thought rater meant to miss or to fail. How does it mean ruined here?

You are right that rater often means to miss (like a train) or fail (like a test). However, when applied to a physical object you are making or a recipe you are cooking, it means to botch, mess up, or ruin it. The blacksmith failed at making the sword, so he ruined it.

Why is le soufflet singular when the English translation says the bellows?

In English, bellows is a plural noun used for a single tool, similar to how we say scissors or pants. In French, un soufflet is a standard singular noun. If you used the plural les soufflets, it would mean the blacksmith was using multiple bellows at once.