I think the answer provided in the old thread someone linked is inaccurate. I've never heard of a significant independence movement in Alsace before 1871 (I may be wrong but the answers don't provide sources so for now I'll stick to that).

The inhabitants of Elsaß-Lothringen were definitely angry at the Reich though, as can be seen in electoral results : until 1890, every single representative to the Reichstag from this Land was a "protesting representative" (député protestataire), and they remained the majority at every election. The main demand of those representatives was a plebiscite on the annexation, which never happened. Meanwhile the representatives of Alsace to the French parliament, elected in 1871, collectively expressed their refusal of joining Germany in a resolution (of course as French politicians they were those who had the most to lose from the annexation).

There are many reasons why the annexation was bad for Alsace. They left the fairly liberal and business-friendly Second Empire to join an authoritarian regime. They left a catholic country for one where the ruling class was dominated by protestants. In France, they had zero autonomy like all other French départements (régions didn't exist then). In Germany, they had zero autonomy but all other Länder were self-ruled (they finally got a Landtag (parliament) in 1911, but no government).

The reason why the Prussian military wanted the annexation was to create a buffer zone between the Catholic countries in Southern Germany (perceived as unreliable) and France. As a result, the region was heavily militarised, and the population felt oppressed and expressed it through the media and its elected representatives. The best-known incident is the Saverne affair in 1913. It worsened during the war, as Alsatians and Lorrains were suspected of French sympathies.

Finally, the population displacement consecutive to the annexation crippled the economy in the short term.

As for the annexation of 1918 : there wasn't a plebiscite either. The Landtag, after sort of declaring independence, did approve its own dissolution and the reunion to the French Republic, but French troops were already occupying the region. At the same time, Marxist revolutionary committees had formed in Elsaß-Lothringen like in the rest of Germany, and those people definitely didn't want to be annexed by France. All of this happened over only a couple of weeks in November 1918, so it's hard to tell what the population really wanted. The representatives to the French parliament collectively declared how much they liked to have joined France, and that there was no need of a plebiscite since not a single list in the 1919 elections was against the annexation (I can't verify that claim, sorry). Their argument sounds a bit jesuitic to me, to be honest.

The French government proceeded to make the whole region (schools, media, administration, signs...) switch to French overnight, and deported all Germans who had settled there since 1871 (triggering complaints from the US), which crippled the economy again. On the other hand, the representatives were able to negotiate a special status for the three départements of "Alsace-Moselle" (basically they kept the German laws they really liked). The best-known feature of this is the lack of separation of churches and the State in those départements. So while in 1871 Alsace-Lorraine ended up with a worse status than other German regions, in 1919 they ended up with a better status than other French regions.

Edit : I'll add that there was a minority autonomist movement in Alsace after WW1 but after its leaders associated with the Nazis during WW2 it lost any support it had. The German Wikipedia claims they overwhelmingly won the elections but it is complete bullshit. No Alsatian autonomist was ever elected to the French parliament.

This has been asked before- TLDR No-one bothered to ask them.