Perhaps you'd be interested more in the Liberal-Conservative debates. I don't mean contemporary politics, but in the 1850's to 1920's, in the UK, politics was mainly a contest between the Tories and the Liberals (in the next party system, the Liberals are replaced by the Labour Party). The Liberals are, unsurprisingly, the party of classical Liberalism--indeed, they're the party that defines classical liberalism. They are both economically and politically liberal, favoring free trade, social reform, and minority rights (here, the minorities were all religious minorities--"Nonconformists" like Quakers, Puritans, and Methodists, as well as of course Catholics). The free-trade position of the Liberals was particularly emphasized when the Peelite pro-free trade wing of the Conservative Party split and joined (or really help found) the Liberals in 1846. In general, the Liberal party supported the emerging industrialists, who wanted low tariffs for cheap raw material and cheaper exports, over the old landed elites, who wanted high tariffs to maintain high agricultural prices. This tension between industrialists and the old landed elite was an important one throughout Europe. This got solved in a variety of ways (cf. Bismark's famous "Iron and Rye" coalition, that is, a coalition which brought together industry and the Junker class of landed elites), but often it meant that the industrialists and landed gentry were on opposite sides of the political spectrum in some European countries, at least until the rise of various kinds of socialism.

Indeed, if you read the history parts of the Communist Manifesto (it's certainly an interesting read, even if not very historically accurate), the bourgeoise appear as the heroes for much it! They're the ones who overthrow the old feudal system. Now, I don't think people would necessarily call them "Right" and "Left" as those terms derive from the French Revolution, but if we think in terms of "standing athwart history, yelling 'Stop'" (as the great William F. Buckley characterized Conservativism) vs. conscious "social reform", as late as the 19th and in some places well into the 20th century, the "capitalists" and industrialists were very often in parties that were on the side of social reform.

The phrase "Left and Right" comes from pre-revolutionary french politics. During the Estates-General, the supporters of the old social order sat to the right of the king, while the revolutionaries or otherwise reform-minded sat on his left. The seating arrangement whereby the party of "progress and change" sat on the left and the party in favor of conserving the old social order sat on the right continued after the estates-general was replaced by the National Assembly, and was maintained up to the restoration.

Capitalism, or the principle by which private citizens own the means of production, has existed since the Bronze Age Collapse and the end of the Minoan Palace Economy (probably earlier!) even if it was only expressly called as such in the mid 19 century, notably by Marx and Engels in their elaborations on their alternative economic system (Communism). Even in societies like Ancient Rome, where the Roman State was a major creator of demand (and redistributor) in the economy, or Merovingian France, where the ownership of land was coupled with responsibilities to the sovereign or overlord, the concept of private ownership never excluded what could be considered the means of production. Because the concept of private ownership extendable to the means of production predates inclusive democratic politics, it was never viewed as a leftist movement.