His presence varies from episode to episode, but its very good even in parts that he isn't in.
Here's an article about it with quote from the Heap:
There will be one obvious difference between series one and two, though: there will be no Dawn French. As we know from the Christmas special, French's character, the loveably wayward Caroline Arless, has left the village of Lark Rise. French was too busy promoting her autobiography and doing a comedy tour with Jennifer Saunders to take part in the second series. Mark Heap, who plays the stiffly withdrawn postman, Thomas Brown, says French's hearty wit is missed on set (and, he adds jokingly, "The food [for the cast] isn't as sumptuous this time, I've noticed").
Whatever the merits of this theory, the characters in Lark Rise are certainly well-mannered – which pleases Heap, as it means that this is the first programme he's been in which he's happy to watch with his 11-year-old daughter. (He's previously been in edgy comedies such as Channel 4's Brass Eye.)
"It gives you a nostalgic hankering for simpler things," he says. "In Lark Rise an engagement can last four years and they've barely held hands. Whereas these days, they're all on Jeremy Kyle."
I didn't know he had a daughter. You learn something new every day.