Bismarck was willing to leave the French a freehand in Africa in the (ultimately delusional) hope that would make them forget about Alsace.
However, the fact that France was able to anticipate Italy in Tunisia dependend much on local dynamics Germany wasn't willing to interfere on at all. A quicker and smarter Italian action could bring Italy in a de facto situation of local control and there was a point where France won't be able to reverse it without war, exactly the opposite of OTL. Neither country would go to war over Tunisia: Italy wouldn'y, and didn't, because she would have been isolated as an aggressor. France wouldn'y, because it would have likely been casus foederis for German and Austrian intervention on Italian side, and France was isolated as well.
So, if a Tunisian faction call for Italian intervention at some point in 1879-80 Italy would have upper hand. I don't think that Italy would have to leave any other claim she had. At this point, Italy held only a small outpost on the Eritrean coast. Her further expansion in Eritrea happened in the framework of a cooperation with Britain that is probably not changed, unless the Italian forces are so sucked into Tunisia that ecomic concern forbids another commitment elsewhere in Africa. At this point, Britain would have to rely on Ethiopia as the local proxy, intervene directly in the area, and maybe allow for some little French claims.
Tunisia already had a significant Italian population that would increase in case of colonization. Tunisia had the potential to actually become the settler colony Italy was being longing for, taking a part of the emigration stream that went to Algeria, France and the Americas in OTL. Italy tried hard to settle italian colonists in Eritrea and later in Libya, with very limited success.
Ethnic cleansing was required for even those limited and ill-fated attemps to start, and so there would be a Tunisian revolt, followed by brutal repression, land confiscation on a wide basis and following state-support settling, in a way not so different than what the French did in Algeria.
I can see a more frustrated and warlike France, even more isolated internationally, as a consequence. Boulanger could come to power? Adua may be butterflied, and that would hugely impact Italian self-perception and politics, non necessarily in a saner way. Without a defeat, the nationalist frenzy could actually be worse TTL and the anti-democratic forces stronger. I see an earlier war for Lybia, and a more authoritarian rule, even more polarized politics, especially if the tyrant Umberto I is not killed.