Hunts isn't the easiest county to research online as the LDS wasn't allowed to film many parish registers, so very few have been extracted onto the IGI, although more are on the BVRI. But there are a lot of parishes which aren't online and which haven't been transcribed by Hunts FHS, so the only place to check them is Huntingdonshire Archives. Nor is there a Baptism Index for Hunts, although there is a Marriage Index.
Francis Seaton can't be a common name, so I'd be checking every instance of it in Hunts. Who, for example was the Francis who married Sarah Agutter in Huntingdon in 1783?
Hang on, it's lunchtime here in France. Got to put the potatoes on.
What was his marital status when he married in Rutland? Bachelor or widower? Was a parish of residence other than Langham given? If so it might provide a clue as to his origins. Who were the witnesses? Might they provide a clue?
You could check the CALM online catalogue at Hunts Archives at
http://www.cambridgeshire.gov.uk/leisure/archives/catalogue/default.htmThere's a mention of the Stilton Francis in 1810, but there's also a settlement examination of Francis Seaton of Fotheringay Northants at Huntingdon in 1793. Fotheringay is only 7 miles from Stilton. He might be your Francis, he might be your Francis' father, he might be a red herring! But when you're struggling, as you are, then you have to follow up every possibility.
You can check burials in Hunts in the FindMyPast index at
http://www.findmypast.co.uk/search/parish-records/baptisms (click on Burials at the top). Who was Francis Seaton buried at Sawtry in 1804? Sawtry's only three miles from Stilton - I don't believe in genealogical coincidences!
But you should go back one generation at a time, checking out each vital event at a time. Which is why your first task should be to check the Langham marriage entry. If that provides no clues then you need to look at the other events that I've suggested.
And keep asking questions!
David