"(Far) right" and "(far) left" have become political labels that often have little to do with ideology. This is even more complicated by the fact that political spectrum is not one-dimensional, and the same issues may not be necessarily grouped as right or left in the same way as in the US, particularly in a multi-party political system, such as the French one.
Right usually refers to:
- Liberal economic policies (i.e., pro-capitalist policies)
- Greater emphasis on individual freedom, particularly in the economic sphere and vis-à-vis the state interference into private life
- Socially conservative policies (such as opposition to gay marriage, abortion, etc.)
- Support for religious institutions
- More assertive national policy
Left usually implies:
- Support for socialist/communist economic policies
- Greater emphasis on the social good than on the rights of an individual
- Liberal social attitudes
- More secular attitudes vis-à-vis religion
- More support for international integration, erasing borders, etc.
The bullets above are based on American division, but it is easy to see how they can be combined differently and, indeed, how they are contradictory: e.g., liberal attitudes in social sphere are an odd combination with non-liberal (socialist) views on economic freedoms; belief in more open borders is odd, if combined with opposition to economic globalization and free trade, etc.
Macron has emerged as a centrist candidate, exhibiting both liberal economic views and progressive (i.e., liberal) views on social issues. This is why he was able to oust more traditional Socialist and Republican parties (Partie Socialiste et Les Republicains, former UMP). As such he draws his support from the center-left and center-right, but decried as right-wing or left-wing by (respectively) the extreme left and the extreme right, which are mainly represented by Jean-Luc Melenchon and Marine Le Pen. It is fair to say that at the moment French have three-party system, each drawing support from about a third of the electorate (although there are many smaller parties that participated in the elections).
In a way, Macron was elected on a wave of a protest movement against the traditional policies, which were viewed as resulting in economic stagnation and degradation of the level of life. His attempts at reforming the pension system, the government monopolies (such as the train system), the small business, etc. have met many objections, including the infamous Yellow Vest protests (Les Gilets Jaunes). This gave the right and the left a possibility to claim that they care about "simple people", while opposing Macron as "the candidate of the rich". Note that "the rich" in France pretty much describes the 43% of the population paying the income tax, what elsewhere would be called the middle class, college graduates, etc.
Thus, the opponents of Macron are driven more by a desire to remove him from office than by specific ideas of how to solve the France's problems. Populism is by definition constitutes tapping into the popular sentiment, without proposing sensible and working solutions, so the attribution to political left/right is here more of secondary (or even historical) importance.
This situation is not dissimilar to anti-establishment populism of Donald Trump and Bernie Sanders. However, the party allegiance, traditional to the American political system, as well as the mack of any significant political movements alternative to the major tow parties, limit the flux of popular support between the two camps (or indeed their awareness of their similarity to each other).