Did men carry talisman on them against threats or to bring luck during Medieval Times?

The Agnus Dei would be one form of talisman that Catholics would keep on their person as a form of protection. Nevertheless Catholics would call it a sacramental.

The origin of Agnus Deis is a matter of much obscurity. Recent authorities lay stress upon the lack of evidence for their existence before the ninth century. But it seems probable that they had their beginning in some pagan usage of charms or amulets, from which the ruder populace were weaned by the enjoyment of this Christian substitute blessed by prayer.

The symbolism of the Agnus Deis is best gathered from the prayers used at various epochs in blessing them. As in the paschal candle, the wax typifies the virgin flesh of Christ, the cross associated with the lamb suggests the idea of a victim offered in sacrifice, and as the blood of the paschal lamb of old protected each household from the destroying angel, so the purpose of these consecrated medallions is to protect those who wear or possess them from all malign influences. In the prayers of blessing, special mention is made of the perils from storm and pestilence, from fire and flood, and also of the dangers to which women are exposed in childbirth. It was formerly the custom in Rome to accompany the gift of an Agnus Dei with a printed leaflet describing its many virtues. Miraculous effects have been believed to follow the use of these objects of piety. Fires are said to have been extinguished, and floods stayed. The manufacture of counterfeits, and even the painting and ornamentation of genuine Agnus Deis, has been strictly prohibited by various papal bulls. Catholic Encyclopedia

One one wall is an Agnus Dei. This is a wax tablet with the Lamb of God impressed on the front. On the reverse is an inscription recording the papal blessing. These devotional objects were very popular with Catholics in England at the time of the Reformation. Possession of an Agnus Dei was used as evidence that the holder was an obstinate papist.

Here is a video if Pope John XXIII blessing the Agnus Dei in 1959: Pope Blessing Angus Dei (YouTube).

This is a tricky question to answer, both because the answer is a definitive "yes" (and so definitive, in fact, that a cataloguing of instances of amulet- and talisman-use would take thousands of pages), but also because the definitions of words like amulet and talisman are themselves a bit tricky. In some cases, people who made use of these things saw them as amulets, but in other cases they saw them no differently to how we might see the taking of antibiotics.

So far as Jewish communities were concerned, Shalom Sabar has an article called "Childbirth and Magic: Jewish Folklore and Material Culture" (in David Biale's Cultures of the Jews), which gives a fairly comprehensive overview of the use of these types of amulets and talismans in late mediaeval Jewish history, and Abraham Green's Judaic Amulets catalogues over 1,000 instances of Jewish amulets of all descriptions. Many of these are still in use today by Jews from North Africa and the Middle East, as well as (to a more limited extent) some Eastern European hasidim.

Jewish sources, like the Shulchan Arukh (which is a 16th century legal code, produced in Ottomon Palestine by Rabbi Yosef Caro) contains some information on which types of amulets are impermissible, and since they are impermissible by virtue of their being considered non-Jewish, such lists also provide us with a bit of information concerning the sorts of things that Christians and Muslims at the time believed to be efficacious. I say "a bit of information", since many of these lists are derived from earlier Jewish sources, and may no longer be reflective of contemporary Christian or Muslim practice.

Prof Hyam Soloveitchik has a beautiful essay on the diminishment of these forms of religiosity in Jewish communities of the modern era, and I quote:

... [R]itual, which was seen to have a physical efficacy, was mobilized to ward off the threatening forces that stalked man’s every step in a world precariously balanced between the powers of good and evil (sitra ahara). The rituals of defense, drawn from the most diverse sources, were religiously inflected, for the Jew knew that what lay in wait for him was not goblins, as the peasant thought, but shedim, and that these agents of the sitra ahara could be defeated only by the proven weapons of traditional lore. Prophylactic ritual flourished as it served the roles of both religion and science. Its rites were thoroughly intertwined with the normative ones and, to most, indistinguishable from one another. Joined in the struggle for health, for example, were amulets, blessings, incantations, and prayers. In the world now inhabited by religious Jewry, however, the material environment has been controlled by a neutral technology, and an animistic, value-driven cosmos replaced by a mechanistic and indifferent one. Modernity has thus defoliated most of these practices and stripped the remaining ones of their significance. People still gather on the eve of circumcision, but as an occasion of rejoicing, not as a nightwatch (wach nacht) to forestall the forces of evil from spiriting away the infant. A Jewish hospital differs from a Catholic one in the symbols on its walls and in the personal religion of its staff, but not in any way in the procedures of health care. As religion ceased to be called upon to control directly the natural world, many vital areas of activity lost their religious coloration, and, with it, their differentiating force.

• Hyam Soloveitchik, "Rupture and Reconstruction"

Nonetheless, some forms of amulet use persisted. The custom of placing mezuzot on doorposts, or of binding oneself with tefillin, certainly originated as talismans, but persist today as non-talismanic forms of religiosity (in the same way that contemporary Jews still pray, but without necessarily believing that their prayers influence the natural order in the way that such prayers were once thought to do). In the interim period (ie: throughout the middle ages and even into early modernity), these sorts of religious items also functioned as amulets.

As such, there are documented instances of Jewish men going to war with mezuzot in their boots, or with passages from tefillin slung around their necks - even as late as WWI. As has always been the case with these things, their function as amulets also testifies to a certain religious syncretism, and it was not particularly uncommon for people who carried them to also carry something that resonates with a different faith: rosary beads, a wooden cross, a passage from Christian or Islamic scripture, etc.

In summary:

There is a wealth of literature on the use of amulets throughout the period that we refer to as the Middle Ages, and while I've only brought a small sample of information that pertains to Jews during this period, the material that concerns Christians, Muslims and other groups of people fills libraries. If you would like to do some more research - and it's a fascinating question! - I would recommend narrowing down your scope of enquiry to a more precise period of history (eg: 13th century), to a more precise location (eg: Germany) and to a more specific group of people (eg: peasants).

My answer above, inasmuch as it looks at one group of people, took Middle Ages to refer to the period from the 16th-19th centuries, even though many people would consider the tail end of that period to encroach upon modernity. By "Middle Ages", you could also include everything from the 3rd or 4th century on, and that's a whole other kettle of fish.