France in particular has stringent laws defending their Jewish community from anti-semitism, but is a country that seems to have a bad record (according to Amnesty International at least) regarding how they treat Roma, up until today. While not as many Roma were murdered during the Holocaust, is there a particular reason both groups have had such diverging paths after the Nazi regime was dismantled?
I can't speak directly to the Jewish experience, but may be able to shed some light from the Romani perspective:
The first thing to know is that the persecution and genocide of Roma began long, long before the Holocaust. The same is true of the Jewish diaspora, and perhaps some Jewish scholars can chime in to address the comparative aspect of your question, but the key piece of information to take away from this is that there is a long precedent of distrust and the lingering effects of previous traumas. In Wallachia and Moldavia (current day Romania) for example, Roma were held in chattel slavery very akin to Africans in the Americas. There are actually correspondences between Romanian and American slavers and both groups were emancipated within the same decade. In other parts of Europe, there were "gypsy hunts" that called for the torture and murder of Romani women and children, forced deportations to other parts of Europe and to the Americas, and forced religious conversions/persecution [see Hancock, The Pariah Syndrome for specifics]. The point is that by the time of the Holocaust, Roma have had more than enough reason to distrust non-Roma.
As we get into the post-Holocaust period, we have a mixture of horrors to consider: entire subgroups of the diaspora have been wiped out, families have been fractured, and now Europe itself is dividing further along the Iron Curtain. Several Soviet countries begin instituting "boarding schools" similar to those seen for Native children in the United States and Canada, while others push Roma into slums or try to make them into "model communists". A very good, nuance portrait of one of the "gypsy boarding schools" is the Czech documentary "Buried Letters." Essentially even children who do receive a quality education and live in relative comfort pay a price of being removed from their families, cultures, and basically being encouraged to abandon these two VERY important aspects of their identity in order to flourish. The documentary touches on a common complaint that the parents were wary of letting their children go to a boarding school and wanted to keep them away out of fear that their children would be taken from them... unfortunately that came to pass as the school kept their students from communicating with their families.
The second thing to keep in mind is that the Romani diaspora is highly diverse, and what may be true of one group or community is not true for another. I'll caveat that most of the Roma I know are Romani-Americans--people whose families (like mine) who have been in the US for generations and have their own communities and customs that may differ from members of their subgroup in another country--and European Roma who have access to education and the internet. Without delving deep into all the nuances of Romani cultures... it's fair to say that each group makes choices and reacts differently than their cousins, but have a shared set of beliefs, language, and cultural values that ties them together.
I'll segue a bit into the cultural side of the equation that factors into both historical practices and current events. Romani ethnic identity is predicated on one's ties to a community/subgroup, their lineage, and "Romanipe"--being raised Romani and aligning to certain cultural tenants (the marhime codes in particular, which deal with spiritual and physical cleanliness). While there have certainly been people who married into Roma communities, those who left them (my family), children forcibly removed, or merging communities (Jewish Roma for example), there exist a bunch of walls between being "Roma" and having another identity. You can't be Romani without being [insert subgroup], you are Romani first and then [insert nation you live in or your family settled in], you are a descendant of this male relative and also you're from [insert state/city]. I'm not sure if this is true as well to certain members of the Jewish diaspora, but the insularity of Romani culture heavily factors into historical and current persecution.
You've undoubtedly heard every ugly stereotype in the book about Roma, almost certainly reinforced by anecdotes across Europe about horrible gypsies. As always the truth is exceptionally complicated; the Roma have unquestionably been victim to centuries of horrors, but that does not erase human agency or personal responsibility. We have MANY issues in our communities [see Hedina Sijercic for the perspective of a Bosnian Romni]. France, Italy, and Russia in particularly have been ramping up on anti-Roma (and anti-immigrant, anti-Semitic) violence.
Sources/Further Information
The most immediate answer to your question is that Jews have already been generally accepted and well-integrated ( At least by the standards of the era and as much as they've ever been ) in Western European nations particularly, with some measure of contrast to Eastern Europe where the insular culture of the shtetl and religious traditionalism still prevailed to a large degree, partially due to the much stricter discriminatory policies and general oppression of the Tsarist Regime. Although that is not to say you would not be able to find a great many highly assimilated Jews in The Pale of Settlement as well and later on in what would become Poland and Russia, for example. This shift primarily came about as a result of the Haskalah, a movement which was a direct effort by Jewish thinkers to integrate the Jewish communities into broader European culture that was inspired by and coincided with the Enlightenment.
It was during the Napoleonic conquests and the advent of Revolutionary France that many European Jews begun to be recognized as equal nationals, or as close as you could get, at least on paper if not consistently in practice, and were afforded many rights which have previously been denied to them. Without boring everyone with the needless details that would cover a great many events in this period, by the time in which the stage was set for WW1 and WW2 to unfold, significant percentages of Jews living in the territories of Germany, Austria-Hungary and France have already been well-established in many respects socially, economically and sometimes even politically. Which was in fact one of the driving forces behind the resentment and conspiracy theories of the Anti-Semitic 'intellectuals' and popular agitators of the time, Hitler among them.
The rise of Nazi Germany was the greatest setback that Jewish emancipation in Europe has known for arguably hundreds of years, and upon it's disgraced defeat, the few Jews remaining in Europe would initially merely resume the status quo of their hated-yet-integrated existence in the following years. The stringent laws that we see today would not come to pass until much later, in synchronicity with the global conception of human rights and liberalization. I'd imagine that since the remaining European Jews, unlike the Roma, were still living as integrated members of their respective societies and often occupying positions of cultural and social import, that their push for acceptance came more naturally, especially with the aid of the American and British Jewish communities which had means of swaying the normalization process of the defeated Axis nations in their favor, unlike the Roma.
Sources:
Jewish Life in Europe Before The Holocaust, U.S Holocaust Museum
The Haskala, Encyclopedia Britannica
On the Eve: The Jews of Europe Before the Second World War, by Bernard Wasserstein
Jews and the Imperial State: Identification Politics in Tsarist Russia, by Eugene M. Avrutin
Nazi Anti-Semitism: From Prejudice to the Holocaust, by Philippe Burrin
After the Holocaust: Rebuilding Jewish Lives in Postwar Germany, by Michael Brenner