It is significant that the speaker, presumably Frost himself, says that he shall be retelling this story about the two roads "ages and ages hence." That suggests hundreds of years. He must either be thinking that there is life after death or else that his poetry will be read ages and ages after his demise. The phrase "ages and ages hence" also strongly suggests that the choice he made to take one road rather than another was of great significance not only for his own life but for the world. In other words, the choices that all of us make in life have infinite repercussions; they affect our friendships, our careers, the people we marry and the children we may have, the futures of those children, grandchildren, etc., and even the non-futures of the children we might have had if we had chosen a different road. The reason he is telling his story with a sigh is probably because he is remembering what a long, hard road it was he chose. Any old man looking back on his life, with all its disappointments and mistakes and regrets is likely to tell his story with a sigh.
In "The Road Not Taken," the speaker sighs in the last stanza:
I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I,
I took the one less traveled by,
The fact that the speaker is still thinking about the road not taken would be a sign of regret. He is still thinking about the other road--the road he didn't take. Two roads diverged in a wood and the speaker could not take both roads. From the very beginning, the speaker states that he is sorry he could not travel both roads:
Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth;
The speaker wanted to take both roads and he regrets not having been able to do so. He is sorry that he could not take both roads. He stood long examining both roads. He was torn between the two roads.
The speaker has doubts that he should ever come back because "way leads on to way." Then he states that he shall be telling this with a sigh. There is a certain amount of regret. The speaker is telling this with a sigh because he could not take both roads. Clearly, he is torn between the roads. The road not taken is still on his mind. That is a sign of regret. If the other road had been a bad choice, the speaker would not be dwelling on it. Also, the speaker would not be "sorry [he] could not travel both."