There's a lot to discuss in an answer to this question. Let's unpack it piece by piece.

Lincoln and much of his cabinet were supposedly abolitionist

This is not really true. On the eve of the Civil War, most Northerners were not abolitionists, though some were. Abolitionists opposed slavery on moral or religious grounds in most cases and called for the immediate outlawing of slavery throughout the US. Most Republicans (a new party at the time heavily devoted to the slavery issue), were what historians call "antislavery." They did not like slavery as an institution, most often because of its economic characteristics. Slavery meant that a man could profit off of other people's labor without working himself, it meant that some men (the slaves) were denied control of their own economic destiny, and it was seen as a source of unwelcome economic competition in the West. Northerners wanted western lands secured for themselves as a means of providing economic opportunity. Having that land open to slavery jeopardized what Northerners perceived as their collective path to economic prosperity.

In terms of policy, most Republicans acknowledged that the Constitution preserved the legality of slavery in the southern states but they maintained that the federal government had the right to regulate the legality of slavery in western territories which had not yet become states (Southerners flatly denied this). The platform that Lincoln ran on in 1860 called not for the abolition of slavery but for the blocking of slavery in any newly organized territories. Although many in the US, North and South, believed with good reason that this policy would spell eventual destruction of slavery everywhere, Lincoln was not directly challenging the legality of slavery where it existed. He expressed no intentions of trying to force emancipation prior to the creation of the EP. That being said, Lincoln also held firm on his commitment to non-extension of slavery.

was there a plan to put an end to slavery before the war forced their hand?

By force, no. But there were plans for gradual and voluntary emancipation efforts put forth by the Lincoln administration (it should be noted that secession was already underway by the time Lincoln took office, so there wasn't any real chance to try and implement any of these policies before the war). These efforts were specifically tried in the Border States. In most cases this involved trying to entice state governments to voluntarily enact gradual, compensated emancipation plans, sometimes with the prospect of colonization (as in, newly freed slaves would have to leave the US for some other place like Haiti or Liberia) thrown in. It's worth noting that such plans got almost no traction in state governments. The Border States did not want to enact emancipation on their own. In addition to this was the issue of contrabands, meaning Confederate slaves who escaped to Union lines once the war started. Though the Union did put in place plans to retain contrabands and not return them to their Confederate owners, and some of these plans involved granting contrabands freedom upon reaching Union lines, the Confiscation Acts were not an effective or widespread method of emancipation.

the Emancipation Proclamation was declared in part to prevent British and/or French intervention in the Civil War.

This is by and large a misnomer. I suggest you check out this thread on the EP from a couple weeks ago. Here's the quote from my post that is most relevant here:

Both at home and abroad, the EP was very much a political gamble. There was as much chance that the EP would help trigger European intervention as prevent it. Simply put, England wasn't that afraid to support slavery. Where do you think they'd been buying all their cotton for decades prior? Britons did sport large abolition movements and working classes especially disliked slavery but when push came to shove, supporting a government which utilized slavery was not the political suicide you're suggesting. And to put it simply, The British government during the Civil War was chiefly interested in seeing the conflict resolved as quickly as possible. They wanted full trade to resume. Until later in the war (after the EP), the default assumption in Europe was that the Confederacy would win sooner or later anyway. As such, an inflammatory document like the EP could (and to an extent was) perceived simply as an indication that the war would not end soon, would cause a lot of needless bloodshed, and thus needed intervention to help reduce hostilities and hasten the inevitable outcome anyway. In the end Europe did not intervene, but the EP is not the primary cause of that nearly as much as people like to assume.