If the Valois still become extinct in 1589 (certainly not guaranteed due to butterflies), then the Bourbon war against Mantua could take place less than half a century after King Francis I's death. That's not that long; it's half the lifetime of a very long-lived person.
OK. If France holds Milan and is the 1st European military power, then there is not too much of a war because France has a decisive say about the issue, Spain is out of the picture and Austrian Hapsburgs do not have enough military power to deal with France. Anyway, in OTL their involvement (especially invasion of the
Grisons and
Valtelline) was to a great degree related to a need to maintain the Spanish Road which does not exist in AH.
Actually, we may have an interesting scenario which somewhat minimizes the differences with the OTL if we assume (see map #1) that as a final settlement Spain gets Naples and the Duchy of Ferrara (in OTL went under the direct Papal rule in 1597 and, anyway, Este ended up being related to the Hapsburgs but we can have them compensated by some other piece of the Italian territory

). Which means that potentially they have an alternative initial part of the Spanish Road with the landing point in the Kingdom of Naples from where the troops could be marching to Pescara or Bari or some other Neapolitan port on the Adriatic and sail to Ferrara.
In the case of the Dutch Rebellion Mantua becomes strategically important because it secures the shortest way to the Hapsburg-held Tyrol. The only problem is Venetian Republic sticking in between so it is of a paramount importance for the Hapsburgs to get hold of Verona to control the route along Adige River. Now, in OTL by the Treaty of Brussels (December 1516) Emperor Maximilian gave the city to his grandson
Charles V of Spain, who in turn ceded it to France (Francis I). The latter finally gave it back to Venice. If we remove the ceding parts, then the Hapsburgs are holding Verona and Venetian territory is being pretty much split (the rights of a passage are guaranteed, blah blah blah). France is sorely tempted to occupy the Venetian territory to the West of the Lake Garda (map #2 - details) and the simplest way to achieve this goal is to give the Hapsburgs slice of the territory between the rivers Po and Adige and between Mincio and Adige up to the Lake Garda (with Peschiera): Venice is not in a position to fight BOTH France and the Hapsburgs.
Now, as soon as the Netherlands are rebelling, Mantua is the most vulnerable segment of the alt-Spanish Road because border with the French-held territory is secured by Lake Garda. As a result, there can be a serious fighting between France and the Spanish-Austrian Hapsburgs even prior to the 30YW. This, of course, providing that at this stage the French are assuming pro-rebel position, which is not 100% guaranteed: in OTL Francis I gave Charles V a free pass to the Netherlands to crush rebellion in Ghent. This was one of the peaceful periods but the principle was that rebellion against the legitimate sovereign can't be allowed. Of course, in AH France may use situation to grab some pieces of the Hapsburg-held Netherlands.
BTW, as a byproduct, France may occupy (completely or partially) the Duchy of Savoy (had been done during the Mantuan War) and Genoa (had been done on a regular basis) to provide a land link to Milan. Saluzzo and Montferrat could be a compensation to Savoy in the case of the "southern option": French are occupying Nice, Genoa and perhaps Parma.
map #1
map #2