The phrase "I believe perhaps" is correct and usable in written English.
It can be used when expressing a tentative opinion or suggestion.
Example: "I believe perhaps we should consider a different approach to the problem."
Alternatives: "I think maybe" or "I suppose possibly."
He then added: "And I believe, perhaps he is a war hero".
I believe, perhaps archaically, that a chef belongs in his kitchen".
I believe, perhaps naively, that we should judge artists – be they writers, film-makers, or musicians – on their best efforts.
For my hair I use Kiehl's Creme Silk Groom, which I believe - perhaps wrongly - makes my hair look a little less grey.
A Republican Party that both talked about the scale of the fiscal problems the country faces and that offered serious solutions would, I believe, perhaps ingenuously, be rewarded at the ballot box, just as Mitch Daniels, the governor of Indiana, has done surprisingly well despite his stinginess and lack of Obama-like charisma.
And I believe — perhaps he's a war hero.
Yes, I believed — perhaps even still believe — that the writer should not be cramped by the possible consequences of her work.
I believed, perhaps naively, that in the free marketplace of ideas, uncorrupted by special interests, we would usually arrive at a sensible consensus.
In the meantime, I still believe — perhaps foolishly — that sustained attention might create change.
And customers seem to tolerate it, believing — perhaps inaccurately — that toilets aren't as dirty or hazardous as once thought.
If gay men are being portrayed with unrealistic positivity – which I don't believe – perhaps that would go some way to counteract the negative stereotypes that have existed in film and TV for years.
