Without Buckley, there would've been no significant third way in French politics. It was no doubt that Buckley's Examen National had a great influence on the rise of the Democratic Centre. Raised a firm Roman Catholic, Buckley was quick to join the Catholic and internationalist Popular Republican Movement in the 50s and joined it's successor Democratic Centre in the 60s. He soon became a chief ideologue in the new conservative movement opposed to both the Gaullist coalition and the left opposition, as well as a critic of Gaullist Euroscepticism, the overreach of presidential power, and Gaulle's withdrawal from Algeria (as overoceans has pointed out). He no doubt contributed to the narrow victory of Alain Poher in the 1969 presidential election (he was a friend and influence on Valéry Giscard d'Estaing and managed to convince him to support the Democratic Centre). He would be a strong critic of the Mitterand government from 1974-1981, and would be integral in expanding the Democratic Centre into the Union for French Democracy. Giscard's subsequent presidency would dominate the 80s and mix traditional conservatism with classic liberalism.
Without Buckley, France probably never sees the decline of Gaullism as without popular support whipped up by the Examen National, the Democratic Centre is forced into coalitions with the Gaullists and is never able to form an identity of their own. In America, I see Buckley due to his Catholic roots joining the Democratic party. Perhaps we see a rightward shift in the Democratic party and retention of their Catholic base, which strayed to the Republicans as Democrats became more and more progressive and liberal. Buckley's American roots lie in Texas, but I don't imagine he'd stick around there too long due to the large amount of anti-catholicism. I imagine he'd move to the nearby Catholic mecca of Chicago, and can definitely see him aligning with the mayor Richard J. Daley. Richard J. Daley represented the conservative Catholic Democrat, and I can definitely see him as having a greater influence on the Democratic party with the support of Buckley if he becomes the chief conservative idealogue for the party. I see a relationship similar to the Giscard-Buckley one, and maybe we get a president Daley in the 80s as well.