I can't think of any example but because the main powers of the co-princes are procedural in nature and often exercised conjointly with the head of government, it's difficult to imagine a scenario with a clear-cut alternative between favouring French and favouring Andorran interests.
In effect, the co-princes now (the current – and first ever – constitution of Andorra dates from 1993) have a role very close to that of a weak head of state in a parliamentary democracy, formally calling new elections in predefined circumstances, etc. One way in which they can indirectly influence the legislative process is by requesting a preliminary judgment on the constitutionality of a proposed law.
But here again, they have no direct influence on policy: For such a request to be successful, the law has to be unconstitutional in the first place and the Constitutional Tribunal has to agree with that. In most European countries, the power to request a constitutional review is discretionary anyway.
Also, because Andorra is so tightly integrated with its neighbours and so dependent on its favourable tax regulations, it's difficult to think of a significant policy area that does not involve France (albeit obviously in minor way, because Andorra is so small). Recusing from rulings that involve France would therefore void the role of any meaning.
It's also easy to find examples of rather heavy-handed involvement in Andorran affairs by the two co-princes. In the 19th century, Andorran politics were dominated by a conflict between two factions variously used as proxy by each co-prince, who were themselves at odds with each other (during this period, France did not always have a president but also two emperors and three kings).
In the 1930s, French gendarmes were sent to secure the first elections after the introduction of universal suffrage. There is no obvious conflict of interest here, as many people in Andorra also wanted universal suffrage, but it still represents a direct involvement of France without the formal consent of Andorra and against some of its institutions, especially the Tribunal des Corts (which opposed the change and initially seemed to expect the backing of the co-princes against the parliament).
A very odd episode took place one year later, when a Russian national got himself elected “king of Andorra” after basically buying the necessary votes in the parliament. This time Spain intervened (at the behest of the Spanish co-prince, the bishop of Urgell, who obviously has no military or police force of his own). Here again, it's difficult to discern what the stake of the bishop in all this was, so no clear conflict of interest per se but Boris the 1st was apparently quite popular with the public and he was deposed by outside forces.
More recently, Nicolas Sarkozy publicly criticised Andorra for its banking and tax policies and somehow threatened to lay down his position as co-prince if nothing changed (why that would be threatening to Andorra, I don't quite follow, but that's what he said and it was meant as a show of strength). It wasn't a “ruling” or formal decision in his capacity as co-prince but he certainly wasn't shy about demonstratively defending the interests of France against Andorra. I think some Andorran politicians boycotted his visit as a result.