As swallow said complex. Very complex. It all depends on what sort of manuscript you're working on. What emotional atmosphere do you need/want to create?
Frutiger is designed for legibility and legibility only. Which makes it a good choice for technincal information, charts etc. Anything where emotions play no role and only the facts count. I would never choose it for say book text or commercial printwork. For the same reason I would also not use it for headers.
That said, if you are thinking of a serif type in combination with the Frutiger I would go for a very 'simple/minimalistic' one. I mean as less fancy as possible, to avoid a conflict with the 'factual' character of the Furtiger. The Clarendon [Light] represents the sort of type I mean. Not 'strong' enough? Think about a slab-serif like the Stymie.
Complex, like swallow said. Complex.
Have fun and ... be nice to the cats
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Relax ... it is just a font