Initially, Alan's clothes indicate to Captain Hoseason that he is a Jacobite. He has a Scottish accent, but he's dressed like a Frenchman. Bonnie Prince Charlie's 1745 uprising against the English throne began in France but then moved to Scotland and the Highland clans. So Alan's clothes provide an easy way of identifying his politics.
At Kidnapped continues, however, the clothes become a larger symbol of what Alan hopes to achieve. Davie has something to reclaim by the end of the novel: his inheritance. He hopes to wind up back at Queensferry where he started. Alan, on the other hand, is wanted for desertion from the English army and rebellion against the king. Even if he manages to beat the murder rap for Colin Roy of Glenure, he'll still be convicted of treason if he gets caught in either the Highlands or the Lowlands. His own country of Appin is too dangerous a place for him to stay. So Alan needs to get back to France.
With the goal of reaching France, Alan has a reason to keep pressing on across the Highlands with Davie. His certainty of reaching France, and his vanity about his appearance once he gets there, becomes clear when he becomes furious with his kinsman, James Stewart, for suggesting that he change his clothes to be less conspicuous while he's on the run. Alan also relies on a French letter of commission in the army as proof that he's not an English deserter, but a French soldier – though whether this would stand up against a military court seems pretty unlikely to Davie (and to us).