Fortuyn was leading in the polls before he was killed. A failed assassination attempt -- by a far-left radical, too -- will serve to vindicate his ideas, and lead to sympathy votes. 45 seats out of 150 in the Lower House isn't out of the question. GroenLinks (Greens) and the PvdA (Labour) will be decimated, even moreso than in OTL. The VVD (centre-right) will take a massive hit, too. But we must keep in mind that people walking away from the left in disgust after their hate-campaign against Fortuyn led to this shocking murder attempt won't suddenly vote for Fortuyn. They'll vote more centre/centre-right, whereas people from those parties will switch to Fortuyn in sympathy.
CDA (Christian Democrats) will be the other winner, because they were the only mainstream party who didn't attack Fortuyn. SGP (conservative Protestants) are small, but may also get an extra seat.
ATL election outcome, if you ask me:
LPF: 45
CDA: 44
VVD: 18
PvdA: 16
SP: 9
D66: 5
GroenLinks: 5
CU: 4
SGP: 3
LN: 1
This would mean LPF and CDA can form a two-party coalition, and there's very little doubt they will. This allows Fortuyn to make an obvious deal, which he was angling for in OTL anyway: the coalition's governing platform leans strongly towards his favoured policies, but most of the top positions will go to CDA politicians. He gets his way, but they get the cushy jobs. Furthermore, instead of putting LPF people in a lot of positions (like undersecretary jobs), Fortuyn will court accomplished businessmen & the such to take over those positions "for one term, to get the house in order". These extra-parliamentary "crisis managers" will get a broad mandate to shake up the bureaucracy and execute mass lay-offs in their departments.
Fortuyn will no doubt flip on the Joint Strike Fighter project, which ensures he doesn't rock the boat when it come to relations with the USA. He favoured more money for NATO commitments, so that'll go over well, too (the CDA agreed, by the way).
Immigration-wise, he'll get his way, too. He'll close the borders almost entirely, but in return, he'll introduce the general amnesty for all immigrants already present. They just gt citizenship, and no more bullshit. But after that: the borders are closed. And from then on, asylum seekers will only be housed in specialised refugee centres in the region they came from. No more will ever be housed in the Netherlands. (The funding for the "international refugee housing" programme will be generous, to forestall complaints from humanitarians. They'll still whine, but the CDA will be ready to agree, so it'll happen.)
All of this will cause problems with the EU, but the Netherlands are the main import gateway for North-Western Europe. In OTL, Orban can tell Brussels to fuck off, and they do in fact fuck off. Fortuyn would be in a much stronger position, so despite much whining from Brussels, he can literally say "shut up or we unilaterally exit the EU within the year". And they'll shut up. In fact, Dutch payments to the EU will be renegotiated, and they'll be lowered.
Taxes will be lowered, although not by as much as he wanted. In the early days of the OTL Balkenende (CDA) government, there was support for comprehensive tax reform. I think with Fortuyn and Balkenende governing together, you might see that happening, possibly with a flat income tax getting introduced, and all loopholes being eliminated.
A return to (an updated version of) the "old" medical inurance scheme would also have broad support. Return of the Ziekenfonds! They'd justify it by saying that with mass migration halted, it'd be fiscally possible to have such a system. I have serious doubts, and I think it'd end up being a mess. But then again, the OTL system is a mess, too. (Too be clear: Fortuyn's idea was a lot like what Singapore does. You have basic payments, and for tht, you get basic service. Want extras? Then pay extra!)
Other things that would be done: infrastructural works would be done (lots of road construction), left-wing activist clubs would be stripped of funding, legislation would be passed to target far-left radicals and to block them from stopping all sorts of building projects with legal actions, and the building of at least one new nuclear plant would get started (probably in North-East Groningen). Finally, Fortuyn and the CDA both felt that the agricultural sector needed reform. This would end up involving a series of reforms that would aid the farmers and cut away regulations that would (as in OTL!) end up strangling thew whole sector eventually (which i happening right now, in OTL).
Fortuyn's plans to reform pensions wouldn't go through. Too many vested interests to let that happens. His plans to reform the military would be off the table, too. Likewise, his plans to reverse the up-scaling of municipalities would be dismissed as "no longer possible", but he'd stop future forced mergers, thus preserving a bit of local government. His plans to up-scale the provinces instead, and to merge them with the waterships, would not happen. (There would be lots of talk about it, but it would come to nought.)
The LPF was a hastily-assembled gaggle of very mixed quality, of course. But I think thry can be kept in check, mostly. The coalition will have a big enough majority that they can handle a few idiots splitting off after stupid in-fighting. Come next election, Fortuyn will have had a few years to weed out the morons and get some better people on board. So "Professor Pim" can stay in charge for quite some time, I think. He'd be divisive, controversial, but he'd have the majority to actually get things done. To many, he'd be a breath of fresh air.
The thing about Fortuyn is that he was a lot more moderate and flexible than his opponents claimed. He'd be in a much better position to form a stable coalition/government than (say) an ATL victorious Jörg Haider, Jean-Marie Le Pen or Filip Dewinter. Fortuyn getting to carry out a lot of his plans would also negate the rise of Geert Wilders. Most of the issues at hand would, t least a meaningful extent, be solved.
The left would forever hate him, the way they also forever hate Thatcher. Internationally, he'd be controversial in many quarters (and most of all in Brussels). But to many in the Netherlands, he's be the man who actually got things done. Not perfectly, not always without problems, nor even without some serious failures... but he actually rolled up his sleeves and got to work. And to the Dutch, at the end of the day, that's where you win popular acclaim. (Which was what Fortuyn, ultimately, desired: to be recognised, and even loved, after having been dismissed by the establishment for so long.)